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$25-34=$ Evaluating Logarithms Evaluate the expression.$${ (a) }\log _{3}\left(\frac{1}{27}\right) \quad \text { (b) } \log _{10} \sqrt{10} \quad \text { (c) } \log _{5} 0.2$$

$=-1$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

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$25-34=$ Evaluating Logari…

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Evaluate the expression.

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Evaluate each expression.<…

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evaluate each expression.<…

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Evaluating Logarithms Eval…

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(a) $5^{3}=125,$ so log _,…

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Evaluate each logarithm. <…

00:57

Evaluate each logarithm.

in this question, we're going to make use off to logarithmic rules. The 1st 1 state that if the base and the value or the same, then the whole log becomes one, right? The other rule that we need here is that lock off a base A with the value B to the power off. See will become. See Look a be right. So take note If this when these two are the same, then the whole lock becomes one. When I have the value to an exponents, the exponents goes, multiply in front and you still have the lock off a B. So in this case, we we have log base three off 1/27. First of all, we can change the 27 into three cubed right, three to the power of three. And to get it into the numerator, I changed the sign off the exponents so it becomes three to the power off. Negative three. Now, from the second through the negative three in the exponents can multiply in front. And I have lived lock based three off three which I've seen from the first rule. This whole log is equal to one. So the on today is negative. Three in lock by staying in the square it often right when we have a square it off something it is that value to the power off 1/2. Why is that? Because the team has an imaginary experiment off one which you can't see. And if there's nothing in a square, root this a little to the right. And remember, with exponential rules, this the root is in the in the denominator. Right? So now the half multiplies in front. We have lived locked to the bites off 10 10 which gives us one. And that ends up to be hope for the last one. We have lock to the base 50 come up to what will happen to this year. Oh, come on to that is to over 10 which simplifies to 1/5. And remember, now that the 1/5 as and exponents off one under five and to get that again into the numerator, it's going to be five to the power off. Negative one. So now I bring with negative one to the front and I have logged 55 which is one m on today is negative one

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