Q. 84 - Precalculus Enhanced with Graphing Utilities

Question

If $5^{-x}=3$ , what does $5^{3x}$ equal?

Step-by-Step Solution

Answer

The vale of $5^{3x}$ is $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.$.

Step 1. Given Information

$5^{-x}=3$

We have to find $5^{3x}$

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

$5^{3x}={\left(5^x\right)}^3={\left(5^{-x}\right)}^{-3}$

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

${\left(5^{-x}\right)}^{-3}={\left(3\right)}^{-3}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$33$}\right.=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$27$}\right.$