for-the-following-exercises-condense-to-a-single-logarithm-if-possible-ln-7ln-xln-y

Question

For the following exercises, condense to a single logarithm if possible.
$$
\ln (7)+\ln (x)+\ln (y)
$$

Lucas Everson · Accepted Answer

Hello. Welcome to the video. And today we&#x27;re gonna be taking a look at natural logs and how we can transform something that may look a little more complex like this and transforming into something that looks a little more friendly in this problem we have the national log of seven was the national log of X. What&#x27;s the natural log of why? And this problem tells us to simplify that now. In order to do this, we&#x27;ll need to know our log properties, and in this case, we will need to know the product rule. And the product rule tells us to that if we have the long or the natural log of a plus the natural log of B, we can rewrite that as the natural log of a Times B. It&#x27;s always important to know that the base value always stays the same. So if this was log a speedy, it would be the same over here and over here, it&#x27;s something to note something that&#x27;s important to remember. So with this in mind, we could go to our problem here and were given national log of seven. What&#x27;s the natural log of X plus the natural log of why we can transform these two into the natural log of seven Times X. And then we had the plus. Why here? And then once again, we could do the same thing and transform these two into our final answer right here. The natural log seven x Y.

K B · Answer

So here we have natural log. A mine is not the log. The mike&#x27;s not to walk, seek and to rewrite. This is a single longer than so, Ellen A We&#x27;re gonna use that day right here on since we subtract ln d and Ellen. See, that means we&#x27;re gonna be dividing by DNC inside the locker room, so we end up with not too long of a over D. C.

Noah Sung · Answer

Okay, so here we&#x27;re given is three lager. Them&#x27;s all subtracted from one another and as to condense them into a single algorithm. Well, if you remember one of the properties of logarithms this one specifically, if we have, um, a lager them log a minus a lot be then you can condense these longer than was into log a divided by B. And so that&#x27;s what we&#x27;re gonna do here. Um, since these are all natural logs, we can combine them, and we&#x27;re gonna start out with this. Um, ln a minus, Helen d first. So that&#x27;s gonna turn into alone over me. We saw this natural log see over here and perform the same, uh, step for these two lager thems. So this is gonna turn into natural log of a over D oversee, right? And since, uh, this since a over these divided by sea, uh, we can ultimately simplify this into a over CD

Lucas Everson · Answer

Hello. Welcome to the video. And today we&#x27;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&#x27;t really matter of one over seven. And the problem tells us to condense this into a single lager. And to do this, we&#x27;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&#x27;s on top minus the law base B of whatever&#x27;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&#x27;s one thing we forgot to include here, and that&#x27;s not work. We&#x27;re not talking about the positive LA base be of one over seven. We&#x27;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&#x27;s your final answer.

Heather Zimmers · Answer

in this problem, we&#x27;re supposed to condense into a single log, a rhythm. So what we want to do is move that negative in front of the LA Guerry them up to be an exponents. And we can do that because of the power rule which says that if you have a number multiplied by your lager, them and that number can come up and become the power on your argument. So that becomes log base be of 1/7 to the negative one. And we can simplify that a little bit more if we recognize that 1/7 is equivalent to seven to the negative one and seven to the negative one to the negative one. Multiply those exponents and we just get seven to the first. So our answer is log base B of seven.

Lucas Everson · Answer

Hello. Welcome to the video and today we will be taking a look at longer rhythms. Today we&#x27;re given log base. Be any value be it doesn&#x27;t really matter what it is of 28 minus log base B seven and we&#x27;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&#x27;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&#x27;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&#x27;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&#x27;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.

Problem

For the following exercises, condense to a single…

Problem 9 Easy Difficulty

For the following exercises, condense to a single logarithm if possible.
$$
\ln (7)+\ln (x)+\ln (y)
$$

Answer

$\ln (7 x y)$

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$\ln (7 x y)$

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