Q. 83 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The vale of $3^{2x}$ is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

Step 1. Given Information

Given :  

$3^{-x} =2$

We have to find $3^{2x}$ .

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

$3^{2x} = {\left(3^x\right)}^2 = {\left(3^{-x}\right)}^{-2}$

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

${\left(3^{-x}\right)}^{-2}={\left(2\right)}^{-2}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$22$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$