Problem

For the following exercises, condense to a single…

00:20

Problem 13 Easy Difficulty

For the following exercises, condense to a single logarithm if possible.
$$
-\log _{b}\left(\frac{1}{7}\right)
$$

Answer

$\log _{b}(7)$

Related Courses

Algebra

College Algebra

Chapter 6

Exponential and Logarithmic Functions

Section 5

Logarithmic Properties

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Video Transcript

Hello. Welcome to the video. And today we're gonna be taking a look at logger rhythms. In this case were given this long here, the negative long base B B could be any value here. Doesn't really matter of one over seven. And the problem tells us to condense this into a single lager. And to do this, we'll need to use the Kocian. Ocean rule allows us to rewrite a log that looks like this into a log that looks like this. So just going through it, if we have log base, be this case, any B could be anything of any value a over any value. See, we can rewrite that as log base. Be even mind that be like the base value here always stays the same. So in this case, it will remain. Is B whatever's on top minus the law base B of whatever's on bottom. So, using this, the context of the problem we can say that log base be of 1/7 equals the law based be of one minus the lawn Base B of seven. So rewriting this again, we can say that this same thing equals, um as we know the log. Oh, the long of anything when one is in the parentheses is gonna equal zero minus log Base B of seven weaken. Keep that the same. So just doing simple subtraction here. This side ultimately equals the negative log base B of seven. Now, there's one thing we forgot to include here, and that's not work. We're not talking about the positive LA base be of one over seven. We're actually talking about the negative. So during some simple algebra, we could just multiply both sides by negative one, and that will make this negative. Go away. And this leads us to our final answer. Our final condensed lotta rhythm. Simply log base B. So that's your final answer.

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