Q. 62 - Precalculus Enhanced with Graphing Utilities

Question

Solve the equation $5^x=5^{-6}$

and verify your results using a graphing utility

Step-by-Step Solution

Answer

Required solution is {-6}

Step 1. Given information

$5^x=5^{-6}$

Step 2. Calculations

$$\begin{gathered} 5^x=5^{-6} \\ x=-6 if a^u=a^v then u=v \end{gathered}$$

So the solution set is {-6}

Step 3. Graphing solution

Graph $y=5^x$ and $Y=5^{-6}$intersect at (-6, 0.000064)

Hence the required solution set is {-6}.