Solving equations Solve the following equations.

Question

log₈ x = 1/3

Accepted Answer

Welcome back everyone. For the given equation solve for Y log of base nine of Y equals one half we're given for answer choices A says three B nine C one and D 81. So for this problem, let's recall the definition of a logarithm. Let's suppose that we have log of base A of number B. And assuming that it is equal to C, we can use an inverse function and we can say that if we take our base A raise it to the power of sea, this would be equal to B. So we are rewriting the exponential form of the logarithm. In this case, we can see that our base A is equal to nine. We also see that the value of B is simply the variable Y and the Sea Valley is one half. So we're going to use the exponential expression starting with A, that's nine. We are going to raise it to the power of C which is one half and this is equal to B which is why well done now nine to the power of one half is simply square root of nine, right? And this would be equal to Y so that Y is equal to three because square root of nine is three and that's it. We have identified the correct answer, which is option A. Thank you for watching.

Solving equations Solve the following equations.

log₈ x = 1/3

Key Concepts

Logarithms

Change of Base Formula

Exponential Functions

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