### Home > INT3 > Chapter 7 > Lesson 7.1.1 > Problem7-9

7-9.

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.

Look at where the variable is in each equation.

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.