Question

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

Answer 1

Solution

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

$\begin{gathered} 13x=156 \\ x=\frac{156}{13} \\ x=12 \end{gathered}$

Therefore the correct answer is 12