SOLUTION: Can you help me solve for x in the equation {{{(log(2, 25))(log(x, 16))=4}}}? Thanks!

Question 275956: Can you help me solve for x in the equation ? Thanks!
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Equations with logarithms are easier to work with and solve when the bases of the logarithms are the same. So we'll start by using the change of base formula, , to change the base of one of the logarithms. Changing the base of the base x logarithm to base 2 looks promising to me because 16 is a power of 2:

Since , . Substituting this in we get:

Multiplying we get:

Multiplying both sides by we get:

Dividing both sides by 4 we get:

So x must be 25!
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