for-the-following-exercises-expand-each-logarithm-as-much-as-possible-rewrite-each-expression-as-a-s

Question

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

Lucas Everson · Accepted Answer

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&#x27;s very important. So I&#x27;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&#x27;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.

Heather Zimmers · Answer

here we have a lager with Mick Expression to simplify, and we&#x27;re going to expand it using the product rule. And you can see that inside the argument of the lager than we have the product. Seven X times, too. Why? So according to the product rule, we can break this up into the log of seven x plus the log of two. Why now? Notice that seven X is also a product, and two why is also a product, So each of those logarithms can be separated into two logarithms as well, So the first logger of them can be separated into log Base B of seven plus log Base V of X and the second law algorithm can be separated into log base fee of two plus log base B of why?

Suzanne W. · Answer

So we are looking at the logarithmic functions and we need to expand the log a rhythm as much as possible and rewrite the expression as a some difference or product of logs. And we have a log based too of why to the X. So recall that the power rule that we&#x27;re seeing here means in general if we have log based b of em to the end, this is equal to end log base, be of them. So this is X log based too, of why?

Lucas Everson · Answer

Hello. Welcome to the video and today we&#x27;re to be taking a look at logger rhythms. This problem were given log base B. Which beacon really equal anything in this situation? It doesn&#x27;t really matter of 13 over 70. The problem tells us to rewrite this Now How exactly we do this, we need to know our log properties. There are quite a few long properties that we know of, but essentially what they do is that they allow us to take logs and rewrite them into different looking logs. But they both equal the same thing. Then they&#x27;re all really important. This we have to use in this problem is tthe equ ocean where if we have a long face B off any value a over any value, See, we can rewrite this into law Base B. It&#x27;s important that we keep the same face value, whatever&#x27;s on top, minus the long face, be of whatever&#x27;s on bottom and these are interchangeable. We can change a log that looks like this into this, and vice versa. And that&#x27;s what we need to do with this problem. So going back to what we&#x27;re given, log base B 13 over 17 could be transformed into our answer right here. Log base B 13 minus log base be 70

K B · Answer

So the first thing I did in this brushes I made the divided by three into 1/3 instead to basically show how we can take this first term on each of these logs and make it be the exponents of what we have here. Maybe and seek. This is just a little longer than to weaken us years. This becomes long based seven of see the fourth Oslo Bay seven of eight of the 1/3 plus Long Bay seven, the beat of the 1/3. And now, since we&#x27;re adding on these logs together, when we write it his single longer than we&#x27;re going to use the same base that will free up. And basically we&#x27;re just gonna multiply. See the fourth by eight of the 1/3 eye view the 1/3 because that will be due in my box. This is gonna be was reading enough about border Eight of the 1/3 beat of the 1/3 seated a fork

K B · Answer

So this question we have a natural log of three a. B in times five seem whereas toe basically put this in the most expanded form that we can using in this case will use Osama box The reason we use a sum of boxes because we&#x27;re multiplying all the terms inside here. So this is gonna be the same as Ellen. Three. Ate pasta Alla and a plus Allenby plus Ellen five plus Ellen seeing. Basically, the reason we got this is because all these things were being multiplied inside the natural lot. We&#x27;ll meet when we write these separate terms being added together. We use addition because of the properties of water.

Problem

For the following exercises, expand each logarith…

Problem 3 Easy Difficulty

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

Answer

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

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

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