College Math CLEP Prep Practice Exam

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When solving log_9(6x), what is the algebraic expression for x?

9 log 6x
log 9 6x
6 log 9x
9^(1/x)

The correct answer is: 9^(1/x)

When solving log_9(6x), we are trying to isolate x. This means that we need to get rid of the logarithm and only have x on one side of the equation. In this case, we take the inverse logarithm, which is raising 9 to the power of the expression inside the logarithm. This gives us 9^(log_9(6x)) = 6x. We know that any number raised to the power of its inverse logarithm is equal to the argument inside the logarithm, which means that 9^(log_9(6x)) = 6x is the same as 6x = 6x. This shows us that x can be any number, and the correct algebraic expression for x is 9^(1/x). Option A, 9 log 6x, is incorrect because we cannot have a