Solve each equation. x = 2^log2 9

Question

Accepted Answer

Hey, everyone in this problem, we're asked to solve the following logarithmic equation. We're given X is equal to nine to the exponent log base nine of 58. We're given four answer choices. All four of them are sets containing one value. Option A has the value of 58. Option B nine, option C nine divided by 58. And option D one, we're gonna start by rewriting the equation we were given. So we have X is equal to nine to the exponent log base nine of 58. OK. So we have kind of a combination here of logarithms and exponentials. OK. This is an exponential equation because we have X is equal to something to some exponent. So recall if we have A is equal to B to the exponent, why we can write this as a log equation? The log base be of A is equal to Y. Yeah. So we can turn an exponential equation into a logarithmic equation where the base of our exponent B becomes the base of our log. Now, in our equation, the base of the exponent is nine. So we're gonna have a log base knife. The A value is gonna be on the opposite side of our equation to our exponent. So our a value in our case is X. So we have a wall base nine of X is equal to everything in that exponent, which is log base nine of 58. Now you might be thinking we had X equals and now we have X inside of a log. How is this helping us? Well, pay attention on both sides. We have log base nine. OK. So if log base nine of X is equal to log base nine of then X must be equal to 58. OK. In order for log base nine to be the same. And so we get that X is equal to 50. This corresponds with answer choice A, that's it for this one. Thanks everyone for watching. I hope this video helped.

Solve each equation. x = 2^log2 9

Key Concepts

Exponential Functions

Logarithms

Properties of Logarithms

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