Question 821895
{{{log( 2, (log(3, (x)))) = 4}}}
When the variable is in a logarithm the first part of solving is finding a way to get it out of the log. When the equation is in the form:
log(expression) = number
like your equation is, then the next step is to rewrite the equation in exponential form. In general {{{log(a, (p)) = n}}} is equivalent to {{{p = a^n}}}. Using this pattern on your equation we get:
{{{log(3, (x)) = 2^4}}}
which simplifies to:
{{{log(3, (x)) = 16}}}<br>
One logarithm is gone. And the remaining equation is in the
log(expression) = number
for so we once again rewrite it in exponential form:
{{{x = 3^16}}}
which simplifies to:
x = 43046721<br>
Last we check. This is <i>not</i> optional! A check must be made to ensure that the bases and arguments of all logs are valid. Use the original equation to check:
{{{log( 2, (log(3, (x)))) = 4}}}
Checking x = 43046721
{{{log( 2, (log(3, (43046721)))) = 4}}}
And we can see that the bases, 2 and 3, and the argument, 43046721, are all valid. So the solution checks.