Upload this document with your Common Application SupplementDental Hygiene Admissions CommitteeDental Hygiene Shadowing FormUNC School of DentistrySupervising Dentist orDate of ObservationName and Address ofDental HygienistNumber of HoursDental SettingSignature ofObservedName:–

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in this lesson we're gonna focus on.solving basic logarithmic equations.let's start with this one log base 2 of.16 is equal to X go ahead and find the.value of X what we need to do is convert.it to exponential form two raised to the.X is equal to 16 now you might already.see the answer but I'm gonna go ahead.and solve it now we know that 2 to the.fourth power is 16 so therefore X is.equal to 4 you can also do this log of.16 divided by log of 2 if you type that.in that's equal to 4 which is X using.the change of base form.try this one log of X log base X of 81.is equal to 4 what is X so let's convert.it to its exponential form X to the.fourth is 81 so now let's find the value.of x to do that we need to take the.fourth root of both sides so the fourth.root of 81 is equal to 3 because 3 to.the fourth is 81 now what about this one.log base 5 of X is equal to 3 convert it.to its exponential form 5 to the third.is equal to X that's 5 times 5 times 5 5.times 5 is 25 and 5 quarters is a dollar.25 so 25 times 5 is 125 let's try some.more examples.log base 32 of X let's say it's equal to.4 over 5 go ahead and try this one so 32.raised to the 4 over 5 is equal to X and.what is that equal to.what is 32 raised to the 4 over 5 how.can we simplify this exponential.fraction so first you want to find the.fifth root of 32 and then raise it to.the fourth.so what number multiplied it by itself.five times is 32 two to the fifth power.is 32 so therefore 32 to the 1/5 is 2 so.now we got to find out what 2 to the.fourth is equal to 2 to the fourth is 16.and so X is 16 here's the next one log.base 3 of 5x plus 1 is equal to 4 find.the value of x so let's convert it to.its exponential form 3 to the fourth is.equal to what's inside and 3 to the.fourth is 81 let's subtract both sides.by 181 minus 1 is 80 and if we divide by.5 80 divided by 5 is 16 so that's the.value of x if log X is equal to 24 what.is the value of x now we don't have a.base if there are no base is written.it's assumed to be base 10 so this is.going to be 10 raised to the 24th which.is a very very big number so I'm going.to leave it as 10 to the 24th now what.about this one Ln X is equal to 7 what.is the value of x natural logs have the.base e so e to the 7th is equal to X and.that is the answer now if you want the.decimal value X is approximately one.thousand ninety 6.63 try this one log.base seven x squared plus three X plus 9.is equal to two.so let's convert it to its exponential.form 7 raised to the second power is.equal to what's inside that is it's.equal to x squared plus 3x plus 9 7.squared is 49 and let's subtract both.sides by 9 so 40 is equal to x squared.plus 3x.let's move the 40 to the right side so x.squared plus 3x minus 40 is equal to 0.now what two numbers multiply to.negative 40 but add to 3 this is going.to be 8 and negative 5 so this can be.factored 2x plus 8 times X minus 5 so X.is equal to negative 8 and positive 5.let's try this example the natural log.of 3x minus 2 let's say it's equal to 5.what is the value of x so keep in mind.the base is e so e raised to the fifth.power is equal to the stuff inside that.is it's equal to 3x minus 2 so now let's.get X by itself so let's add 2 to both.sides so e to the 5th plus 2 is equal to.3x and if we divide by 3 X is equal to e.to the 5th plus 2 over 3 and as a.decimal.this is approximately fifty point one.four let's try one more example four.times the natural log of 2x minus one.plus three is equal to eleven go ahead.and find the value of x so let's begin.by subtracting both sides by three so 11.minus three is eight now let's divide.both sides by four eight divided by four.is two at this point we can convert it.into its exponential form so e raised to.the second power is equal to 2x minus.one.so let's add one to both sides and then.let's divide by two so X is equal to e.squared plus one over two and as a.decimal that is approximately four point.one nine four five consider this.equation log base 3 5 X plus 2 and let's.say that's equal to log base 3 7 X minus.8.what is the value of x now because the.bases are the same and that means that.the stuff inside of the log must be.equal to each other.so therefore 5 X plus 2 is equal to 7x.minus 8 so now we can find the value of.x let's subtract both sides by 5 X and.let's add 8 to both sides 2 plus 8 is 10.7 X minus 5 X is 2x so therefore X is 10.divided by 2 which is equal to 5 and.that's all you need to do for this.example so now it's your turn I try this.example let's say that log base 2 of x.squared plus 4 X is equal to log base 2.of 5 feel free to pause the video so.because the bases are the same that.means that x squared + 4 X must equal 5.now we have a quadratic equation so.let's move the 5 to the left side it's.going to be negative 5 or on the left.and now let's factor and what two.numbers multiply to negative 5 but add.to the middle term for this is positive.5 and negative 1 so we have X plus 5.times X minus 1 is equal to 0 so X is.equal to negative 5 and X is equal to 1.and so those are the answers now let's.work on a different example log base two.of X plus log base 2 of X plus four is.equal to five go ahead and calculate the.value of X now let's review a basic.property of logs log a plus log B is.equal to log eight times B we need to.use this equation to combine the two.logs into a single log.so if log base two of X plus log base 2.of X plus four is equal to five then log.base two of X times X plus four and that.has to be equal to five as well so now.let's convert it to its exponential form.2 to the fifth is equal to what's inside.unless distribute the X so x times X is.x squared.x times 4 is 4x and 2 to the fifth power.is 32 so now let's move the 32 to the.other side it's positive on the left.side which means it's negative on the.right side so now let's factor what two.numbers multiply to negative 32 but add.to 4 so we have 8 and negative 4 so this.is going to be X plus 8 times X minus 4.so X is equal to negative 8 and positive.4.in this example we need to check the.answers.we need to check for extraneous.solutions if we replace X with negative.8 notice that this is not gonna work you.cannot have a negative number inside a.log and you could type it in your.calculator type in log negative 8 it's.going to give you an error so this.answer is it doesn't work now let's plug.in 4 so log base 2 of 4 plus log base 2.of 4 plus 4 which is 8 is that equal to.5 well we know 2 squared is 4 so log.base 2 of 4 is 2 log base 2 of 8 is 3.because 2 to the third power is 8 and 2.plus 3 is indeed 5 so that works try.this one log base 3 of X plus 1 let's.say it's equal to 3 minus log base 3 of.X plus 7 so what do you think we need to.do here in this example we cannot set X.plus 1 equal to X plus 7 because of the.3 here.however we could take this log and move.it to the side and it's going to be.similar to the last problem if we do.that so it's gonna be positive log 3x.plus 7 so now we can combine the two.logs into a single log by multiplying.this stuff on the inside so we need to.multiply X plus 1 times X plus 7 so now.let's convert it to its exponential form.3 to the third power is equal to the.stuff inside let's go ahead and foil X.plus 1 times X plus 7 x times X is x.squared X times 7 that's 7x and then we.have 1 times X which is x + 1 times 7.that's 7 3 to the third power is 27 7 X.plus X is 8x and now let's subtract both.sides by 27.so we have zero on the left and seven.minus 27 is a negative 20 so what two.numbers multiply to negative 20 but add.to the middle number 8 this is going to.be 10 and negative 2 so we're gonna have.X plus 10 and X minus 2 so X is equal to.negative 10 and positive 2 so let's see.which one works and which one does not.work so the original equation is log.base 3x plus 1 which is equal to.everything on the right side so we can.see that negative 10 is not going to.work if you plug a negative 10 negative.10 plus 1 is a negative number and we.cannot have a negative number inside the.log if we plug into 2 plus 1 is 3 2 plus.7 is 9 that's okay so 2 is gonna work.that's the answer so here's another.equation that you'll see as well so this.time instead of having a plus sign in.between the two logs we're gonna have a.minus sign and if you recall log of a.minus log of B is equal to log a divided.by B so we need to combine the two logs.used in division so we're gonna write it.as a single log and the one that's.positive is going to go on top that is.2x plus 6x minus 1 has a negative sign.in front of the log and all of this is.equal to 1 so now let's convert it to.its exponential form 4 to the first.power is equal to what's inside so.that's equal to 2x plus 6 divided by X.minus 1 4 is the same as 4 over 1.so now let's cross multiply 1 times 2x.plus 6 is 2x plus 6 and 4 times X minus.1 is 4x minus 4 now let's subtract both.sides by 2x.and let's add four to both sides six.plus four is ten 4x minus 2x is 2x and.10 divided by 2 is 5 so this is the.answer and if you plug in 5 into X minus.1 that will give you a positive number.if you plug it into here that will also.give you a positive number so you won't.get any negative numbers inside a logue.so X is equal to 5 this is the last.example for this video feel free to try.it so whenever you have an equation with.two logs and a number you want to get.the two logs by itself on one side of.the equation so let's move this to this.side so log base 2 X plus 3 minus log.base 2 X minus 3 that's equal to 4 so.let's combine this two logs into a.single log use in division the one.that's positive will go on top and now.let's convert it to its exponential form.so 2 to the fourth power is equal to.what's inside.and two to the fourth is 16 so now let's.go ahead and cross multiply so we have x.times I mean 1 times X plus 3 which is X.plus 3 and then 16 times X minus 3.that's 16 X minus 48 now let's subtract.both sides by X and let's add 48 to both.sides so these will cancel 48 plus 3.that's 51 and let's see 16 X minus X is.15 X so if we divide by 15 X is 51 over.15 now both numbers are divisible by 3.51 divided by 3 is 17 15 divided by 3 is.5 so it's 17 + 5 let's say that log X.raised to log X is equal to 49 what is.the value of X what would you do first.in this problem what we can do is move.this in front so we'll have log x times.log X is equal to 49 log x times log X.is equivalent to log X squared and now.what we can do is take the square root.of both sides the square root will.cancel with the square so on the left.it's just gonna be log X on the right.the square root of 47 I mean not 47 but.49 is plus or minus 7 so log X is equal.to positive 7 and log X is equal to.negative 7 now keep in mind the base is.10 so let's convert it into its.exponential form 10 raised to the 7 is.equal to X so X is equal to 10 to the.seventh which is 10 million 10 to the.negative 7 is also equal to X.and so this is the answer 10 to negative.7 is like point zero zero zero zero zero.zero one so it's a positive number and.if you plug in a positive number into a.log there's nothing wrong with that.there's no issue with that.so both answers are acceptable you can't.plug in a negative number inside the log.but these are positive numbers one is.just very large the other is simply very.small here's the next one log of x.squared is equal to log X square what is.the value of x in this problem the first.thing I would recommend doing is moving.to two so this is a two log X you can't.move this two because the tool applies.to everything this two means that you.have log x times log X which is.completely different so we can't move.that two to the front so right now this.is what we have now I'm going to take.two log X and move it to the right side.so zero is equal to log X squared minus.two log X now let's factor the GCF is.log X log X square divided by log X is.log X negative two log X divided by log.X is simply negative two now we can set.each factor equal to zero so log X is.equal to zero and also this part log X.minus two is also equal to zero.now let's be careful because this is log.X minus two is equal to zero the X is.part of the log but the two is not now.the base of log is 10 10 raised to the 0.is equal to X and anything raised to the.0 power is 1 so therefore X is equal to.1 now let's get the other answer.so first let's add 2 to both sides so.log X is equal to 2 and the base is 10.so 10 squared is equal to X 10 squared.is equal to 100 so X is equal to 100 now.let's make sure that we do indeed have.the right answers so let's check each.one and let's write the original.equation which was log x squared is.equal to log X square so let's start.with 1 log 1 squared is that equal to.log 1 squared log 1 is 0 and 0 squared.is also 0 so that is a true statement so.X is indeed equal to 1 now let's plug in.100 log 100 squared is that equal to log.100 squared well we can move the 2 to.the front so this is 2 times log 100 and.log 100 keep in mind the base is 10 10.squared is 100 so log 100 is 2 so 2.times 2 is equal to 2 squared they both.equal 4 so X is indeed equal to 1 and.100 try this log of log.of AX is equal to four go ahead and find.the value of x if you don't see a base.its base 10 so 10 raised to the 4 is.equal to what's inside which is log X.now 10 to the 4 is 10,000 it's a 1 with.4 zeros now keep in mind the base of.this log is also 10 and 10 raised to the.10,000 is equal to the stuff inside.which is X so that's the answer it's 10.raised to 10,000 here's another one like.that log base 3 of log base 2 X let's.say that's equal to 2 so 3 raised to the.second power is equal to what's inside.which is log base 2 of X and 3 squared.is 9 and we know that 2 raised to the.nine is equal to the stuff inside which.is X so X is 2 to the 9th power so what.exactly is 2 to the 9th power 2 to the.9th is 2 to the 4th times 2 to the 4th.times 2 to the first power because 4.plus 4 plus 1 is 9 2 to the 4th is 16 16.times 16 is 256 256 times 2 is 512 and.you can also just type this in your.calculator you should get 512 as well.

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What do you do when you shadow a dentist?

You will learn whatever he is doing inside his clinic, his actions, styles, strategies, skills, doctor patient relationship, and whatever knowledge he has extended on you while shadowing him.

How does it feel to live in India as an atheist ?

I am a teenager living in the metropolitan city of Mumbai and am a partial atheist…why so I will tell you
My mom has a hardcore believe In goddess durga and wants me to believe in them and follow them but I like to take things more logically and think about these things as a result of some mischief/experiment/plot done some greater entities in the past(kind of the stuffs they say in ancient aliens) and thus make me feel hollow inside in a state of deep thought like why were we made and all that BS stuff's.
But sometimes when I am in a state of trouble I do pray (childhood habit by mom) and thing
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Is dental school rolling admission?

If you go to www.owl.purdue.edu, you will have access to Purdue University’s Online Writing Lab, which offers an incredible amount of information about and examples of essay types, and the site includes interactive grammar, style, punctuation exercises, as well as documentation guides for MLA, APA, and other style formats. If you are writing an argument essay, or another type of essay, the site covers the essentials of creating a thesis, supporting the thesis, using quotations, research, and documenting your sources. If you are writing an essay on a controversial topic, go to http://www.pro
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