Problem

For the following exercises, condense to a single…

00:21

Problem 11 Easy Difficulty

For the following exercises, condense to a single logarithm if possible.
$$
\log _{b}(28)-\log _{b}(7)
$$

Answer

$\log _{b}(4)$

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 will be taking a look at longer rhythms. Today we're given log base. Be any value be it doesn't really matter what it is of 28 minus log base B seven and we're told to simplify. This is my sweet hair. Now, in order to do this, we need to know our log properties and this case will need to know the ocean and the ocean rule tells us that if we have a long that looks like this for here, we can rewrite as a law that looks like this and vice versa. So if we have log base, be of any value A and we're subtracting a log of the same base value in this case, be of any value. See, we can rewrite that as log base. Be off whatever's in front. Whatever. The 1st 1 is here, eh? Divided by whatever is second here in this case. See? So these are interchangeable and we'll need this to simplify Here. Going back to the problem were given log base B of 28 minus log base B of seven and because they both have the same base value we can use our rule so we can transform this into law based be off whatever's 1st 28 divided by whatever second, which is seven. And this is a fraction that we know we can transform that four. So that leads us to our final answer. Log base B four.

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