Solve each equation. log￬2 x = 3

Question

Accepted Answer

Hey, everyone in this problem, we're asked to solve the following logarithmic equation for X log base six of X is equal to four. We're given four answer choices. All of them are set containing one value. Option A, the value is 1296. For option B, it's 7776 for option C it's 648 and for option D, it's 4096. Now writing what we have, we have log B six of X is equal to four. Now we have this X inside of our logarithm. OK. In order to solve for X, we need to get it outside of that log. Now, let's recall, we have a rule that allows us to relate log equations to exponential equations. This is gonna give us a way to get that X outside of that lock. So if we have phase B of some value A equal to Y, we can write this as B to the exponent Y is equal to A. OK. So the base B of our log becomes the base B of our exponential. Now the base of our log is six. OK. So the base of our exponential is going to be six. The exponent Y of our exponential is going to be the value that's on the opposite side of the equation as our log. So in our case, that's four, so we get six to the exponent four and this is gonna equal A which is everything inside of the log, which in this case is X. So we have X is equal to six to the exponent four. And if we evaluate that six to the exponent four is equal to 1296. OK. And that is what we were looking for. The correct answer for this one is a 1296. That's it for this one. I hope this video helped see you in the next one.

Solve each equation. log￬2 x = 3

Key Concepts

Logarithms

Exponential Functions

Properties of Logarithms

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