Question 238165
When the variable you're solving for is in the argument of a logarithm, the most common way to solve the problem is to rewrite the logarithmic equation in exponential form. With this problem's log of a log we will have to do thsi twice.<br>
Remember that {{{log(a, (b)) = x}}} is equivalent to {{{b = a^x}}}. We will use this twice in succession on your equation:
{{{log(5, (log(5, (x)))) = 1}}}
which in exponential form is:
{{{log(5, (x)) = 5^1}}}
which simplifies to
{{{log(5, (x)) = 5}}}
Rewriting this in exponential form we get:
{{{x = 5^5}}}
which simplifies to
{{{x = 3125}}}