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

$\ln (7 x y)$

Algebra

Chapter 6

Exponential and Logarithmic Functions

Section 5

Logarithmic Properties

Functions

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

00:21

For the following exercise…

01:48

02:17

00:56

01:49

00:45

01:37

00:47

01:22

00:20

Hello. Welcome to the video. And today we'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's the natural log of why? And this problem tells us to simplify that now. In order to do this, we'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'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's something to note something that's important to remember. So with this in mind, we could go to our problem here and were given national log of seven. What'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.

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