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Combine the given expression into a single logarithm.$$2 \ln x-4 \ln y$$

$$\ln \frac{x^{2}}{y^{4}}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

Campbell University

University of Michigan - Ann Arbor

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Yeah, eso We're going to use, um to law logs in order to solve this problem. Ah Ndure actually have multiple options to do this. What I like to do, though, is to rewrite the numbers in front and just move them as exponents. That's one of the law of logs that were going to use. Um, this is where you actually have two options is you can leave it as a minus, um, and then think about well, if we have a minus and we're trying to combine logs as a single log rhythm, then we combine them using division I've had students actually remember the minus and ah, giant line for a division. If that works for you, then by all means do that. Eso that's your final answer. I do want to point out, though, is another way you can do this now I'm gonna do this quickly is just change it to a plus and keep that negative attached to the four. Well, then you can combine these using edition and what I'm talking about there is when you're adding that you multiply and then you can rewrite this as a negative explode and goes into the denominator. So it's the same answer that might help you

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