### Home > A2C > Chapter 13 > Lesson 13.2.3 > Problem13-136

13-136.

Without using a calculator, solve these two problems from a college entrance exam.

1. If x−4/3 + 1 = 17, find x−1/3.

Subtract 1 from both sides.

$\small x^{-\frac{4}{3}}=16$

$\text{Raise both sides to the} -\frac{3}{4}\text{ power.}$

$\text{Now raise }\frac{1}{8}\text{ to the }-\frac{1}{3}\text{ power.}$

$2$

1. If log(A) = a, find $\operatorname { log } ( \frac { A } { 100 } )$

Simplify the second log.

$\operatorname{log}\left(A\right) − \operatorname{log}\left(100\right)$

Remember that $100$ is $10$ to the 2nd power.

$\operatorname{log}\left(A\right) − 2$

$a − 2$