Q. 82 - Precalculus Enhanced with Graphing Utilities

Question

If $2^x=3$ , what does $4^{-x}$ equal?

Step-by-Step Solution

Answer

The vale of $4^{-x}$ is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.$

Step 1. Given Information

Given : 

$2^x=3$

We have to find $4^{-x}$.

Step 2. Write expression to be found in terms of given expression.

$4^{-x}= {\left(2^2\right)}^{-x} = 2^{-2x} ={( 2^x)}^{-2}$

Step 3. Put the given value in the expression and solve.

${\left(2^x\right)}^{-2} = {\left(3\right)}^{-2} = \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3^2$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$9$}\right.$