document.write( "Question 821895: solve for x:
\n" ); document.write( "log 2 (log 3 x) = 4 -----> log of (log of x base 3) base 2 equals 4
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Algebra.Com's Answer #494616 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"log%28+2%2C+%28log%283%2C+%28x%29%29%29%29+=+4\"$
\n" ); document.write( "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:
\n" ); document.write( "log(expression) = number
\n" ); document.write( "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:
\n" ); document.write( " $\"log%283%2C+%28x%29%29+=+2%5E4\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( " $\"log%283%2C+%28x%29%29+=+16\"$

\n" ); document.write( "One logarithm is gone. And the remaining equation is in the
\n" ); document.write( "log(expression) = number
\n" ); document.write( "for so we once again rewrite it in exponential form:
\n" ); document.write( " $\"x+=+3%5E16\"$
\n" ); document.write( "which simplifies to:
\n" ); document.write( "x = 43046721

\n" ); document.write( "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:
\n" ); document.write( " $\"log%28+2%2C+%28log%283%2C+%28x%29%29%29%29+=+4\"$
\n" ); document.write( "Checking x = 43046721
\n" ); document.write( " $\"log%28+2%2C+%28log%283%2C+%2843046721%29%29%29%29+=+4\"$
\n" ); document.write( "And we can see that the bases, 2 and 3, and the argument, 43046721, are all valid. So the solution checks. \n" ); document.write( "

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