CPM Homework Help : A2C Problem 7-95

Margee thinks she can use logs to solve $56=x^8$ , since logs seem to make exponents disappear. Unfortunately, Margee is wrong. Explain the difference between equations like $2=1.04^x$ , in which you can use logs, and $56=x^8$ , in which it does not make sense to use logs.

Hint:

Look at where the variable is in each equation.

Answer:

Logarithms are used to solve equations where the variable is the exponent.
Roots (or raising to a fractional exponent) are used to solve equations where
the exponent is known and the variable is the base.

Margee should raise both sides of the equation to the $\frac{1}{8}^{\text{th}}$ power.