In Exercises 1–40, use properties of logarithms to expand each lo...

Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.

ln 5√x (fifth root of)

Accepted Answer

everyone welcome back in this problem. We are asked to expand the given logarithmic expression and try to evaluate it by using the properties of logarithms. And the expression were given is log the seventh route of why. Alright now let's recall. We have a log property that deals with exponents. Okay so we know that if we can write this as an exponent we'd be able to use that log property. And now let's recall again that we have a rule that allows us to write roots in terms of experiments. Okay, so let's go ahead and use that. So if we have the end route some value M we can rewrite this as M to the exponent. One over end. Okay. So we can change that route into an exponent applying this to our expression. We have log Why to the 1/7. Alright, so we've written it as an exponent. Now let's recall that log property that allows us to deal with exponents. If we have log base B of something X. To the exponent end, this is equivalent to running n log base B of X. Okay, so the exponent N can come out in front and multiplies to the entire log. So in our case this is going to give 1/7 times log of why? Right. And there's nothing more that we can expand or evaluate here. And so that's going to be our solution. The expression is going to equal 1/7 log of Y. That's going to correspond with answer a thanks everyone for watching. See you in the next video

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln 5√x (fifth root of)

Key Concepts

Properties of Logarithms

Natural Logarithm

Radicals and Exponents

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