SOLUTION: solve for x.... logx64=-6

Question 354710: solve for x.... logx64=-6
Answer by jsmallt9(3758) (Show Source): 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:

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