You can put this solution on YOUR website! With an equation of the form
log(expression) = other-expression
and the variable in the argument or base of the logarithm, then you will usually rewrite the equation in exponential form. In general, is equivalent to . Using this on your equation we get:
Rewriting this with a positive exponent we get:
We can eliminate the fraction by multiplying both sides by :
Next we can divide both sides by 64:
To find x we will find the 6th root of each side:
(Since x is the base of a logarithm in this problem, we can ignore the negative 6th roots of 64. Bases of logarithms must be positive!) Since we get 1/2 on the left side:
(