SOLUTION: Given log(base"a")2=x, determine log(base"16)(a^log(base"a")x)=100. Solve for a. I have simplified the question to (4x)(a^log(base"a")x)=100. I am not sure what I can now do to

Question 375676: Given log(base"a")2=x, determine log(base"16)(a^log(base"a")x)=100. Solve for a.
I have simplified the question to (4x)(a^log(base"a")x)=100. I am not sure what I can now do to solve for "a".
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Given

and

Let's start by looking at: . Once you understand logarithms well you will see instantly how this simplifies. The exponent, , is a logarithm. Logarithms are exponents. This logarithm represents "the exponent for "a" that results in "x". And where do we find this exponent? Answer: As the exponent for "a"! So by definition, is x! The second equation is now:

Into this equation we can substitute for x using the first equation:

We now have an equation with just a in it. We can now solve for a, First we rewrite the equation in exponential form. In general is equivalent to . Using this on the equation above we get:

Rewriting this equation in exponential form we get:

And last we find the th root of each side:

(Since "a" was the base of a logarithm it had to be positive. So we do not need to be concerned with the negative th root of 2.)

The th root of 2 is a very strange answer. Perhaps you made a mistake in posting this problem. I have checked my work and I do not see any mistakes.

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