Question

Hello, I need help with this precalculus homework question, please?HW Q11

Answer 1

Solve the equation

`64^(-x+26)=128^x`

Step 1: Applying exponential rules

`\begin{gathered} 64^(-x+26)=128^x \\ 2^(6(-x+26))=2^(7x) \\ 6(-x+26)=7x \end{gathered}`

Step 2: Evaluate the value of x

`\begin{gathered} 6(-x+26)=7x \\ -6x+156=7x \\ 156=7x+6x \\ 156=13x \end{gathered}`

Step 3: Divide both side by 13

`\begin{gathered} 13x=156 \\ x=(156)/(13) \\ x=12 \end{gathered}`

Therefore the correct answer is 12