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

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for x: log 2 (log 3 x) = 4 -----> log of (log of x base 3) base 2 equals 4       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
log%28+2%2C+%28log%283%2C+%28x%29%29%29%29+=+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%28a%2C+%28p%29%29+=+n is equivalent to p+=+a%5En. Using this pattern on your equation we get:
log%283%2C+%28x%29%29+=+2%5E4
which simplifies to:
log%283%2C+%28x%29%29+=+16

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%5E16
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:
log%28+2%2C+%28log%283%2C+%28x%29%29%29%29+=+4
Checking x = 43046721
log%28+2%2C+%28log%283%2C+%2843046721%29%29%29%29+=+4
And we can see that the bases, 2 and 3, and the argument, 43046721, are all valid. So the solution checks.