Q. 81 - Precalculus Enhanced with Graphing Utilities

Question

If $4^x=7$ , what does $4^{-2x}$ equal?

Step-by-Step Solution

Answer

The value of $4^{-2x}$ is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$49$}\right.$.

Step 1. Given Information

Given :

$4^x=7$

We have to find $4^{-2x}$

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

$4^{-2x} ={( 4^x)}^{-2}$

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

${\left(4^x\right)}^{-2} = {\left(7\right)}^{-2} = \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$7^2$}\right. = \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$49$}\right.$