SOLUTION: solve for x: log 2 (log 3 x) = 4 -----> log of (log of x base 3) base 2 equals 4

Question 821895: solve for x:
log 2 (log 3 x) = 4 -----> log of (log of x base 3) base 2 equals 4

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

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 is equivalent to . Using this pattern on your equation we get:

which simplifies to:

One logarithm is gone. And the remaining equation is in the
log(expression) = number
for so we once again rewrite it in exponential form:

which simplifies to:
x = 43046721

Last we check. This is not optional! A check must be made to ensure that the bases and arguments of all logs are valid. Use the original equation to check:

Checking x = 43046721

And we can see that the bases, 2 and 3, and the argument, 43046721, are all valid. So the solution checks.
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