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For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs.$$\log _{b}(7 x \cdot 2 y)$$

$\log _{b}(7)+\log _{b}(x)+\log _{b}(2)+\log _{b}(y)$

Algebra

Chapter 6

Exponential and Logarithmic Functions

Section 5

Logarithmic Properties

Functions

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

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01:32

In mathematics, the absolu…

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Hello. Welcome to the video, and today we will be taking a look at longer rhythms. This problem were given log base B seven x times, too. Why? And this problem tells us to expand this as much as we can. Now, in order to do this, we need to understand our log and for this particular problem will need to know E product. And the product rule allows us to rewrite along that looks like this into this. So if we have a long based be any value be of two things being multiplied together, we can rewrite it as log base B of this case, X plus law based B off the other thing being multiply in this case why? And the only thing to know is that the face value always stays the same. It's very important. So I'm going to the problem. Were given log base B seven x times, too. Why now? Before I started using the long property, I started to look at this a little differently. Started to take it apart a little bit. We can look at this as long base B of seven times x times two times why and that might make it a little easier to see how we would use the product from so transforming this into our final answer. You have logged based B seven plus log base B of X plus log base, be of two plus law based Be of why so we essentially just take each component that's being multiplied here, attention to a log base B and add them all up to each other, and that is how the product rule works.

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