Question

solve. write your answer as an integer or a fraction in simplest form.\\(\frac{1}{8} = 8^{2x + 4}\\)\\(x =\\)\\(\frac{\square}{\square}\\)

Explanation:

Step1: Express both sides with base 8

We know that $\frac{1}{8}=8^{-1}$, so the equation becomes $8^{-1}=8^{2x + 4}$.

Step2: Set exponents equal

Since the bases are the same, we can set the exponents equal: $-1 = 2x+4$.

Step3: Solve for x

Subtract 4 from both sides: $-1 - 4=2x$, so $-5 = 2x$. Then divide both sides by 2: $x=-\frac{5}{2}$.

Answer:

$-\frac{5}{2}$