Problem

$25-34=$ Evaluating Logarithms Evaluate the expre…

01:49

Problem 30 Medium Difficulty

$25-34=$ Evaluating Logarithms Evaluate the expression.
$$ { (a) }\log _{5} 125 \quad \text { (b) } \log _{49} 7 \quad \text { (c) } \log _{9} \sqrt{3}$$

Answer

$=\frac{1}{4}$

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Algebra

Algebra and Trigonometry

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

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Video Transcript

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 the 1st 1 we have the log based five off 125 and in this case I can rewrite the 125 as five to the power off three. And from the second rule that we've discussed, the three can multiply in front off the locker longer them and we have lift lock based 55 which we've seen is equal to one over on today is three in log base, 49 off, Stephen. But it's the it's more. It's It would be easier to change the saving into something off a 49 thing to change the 49. So if I have a look at the seven, I know that that is actually the square root off 49 right, which is then 49 to the power off. Ah, half. Now the half can multiply in front and when the base and that value of the same that is, the whole log becomes one summer on today is 1/2. So for the last one, we have log nine square root three. So what is the relationship between the three and the nine? I can rewrite the three. So I keep the square root and three on its own is again this square it off. Nine. So the squared off the square root is this squared off nine to the power of 1/2 right which becomes nine to borrow for Hoff to the power off another Hoff which simply Farr's 29 to the power off 1/4. Now the 1/4 can come to the front, multiply here in front off the log and we end up to have 1/4 times one, and that finalizes to 1/4

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