Question

question
solve for x:
$2^5 = 32^{x + 4}$
answer attempt 1 out of 2
$x = $

Explanation:

Step1: Rewrite 32 as base 2

$32 = 2^5$, so $32^{x+4} = (2^5)^{x+4}$

Step2: Simplify right-hand side

Use exponent rule $(a^m)^n = a^{mn}$:
$(2^5)^{x+4} = 2^{5(x+4)} = 2^{5x+20}$

Step3: Set exponents equal

Since bases are equal, $5 = 5x+20$

Step4: Solve for x

Subtract 20 from both sides:
$5 - 20 = 5x$
$-15 = 5x$
Divide by 5:
$x = \frac{-15}{5} = -3$

Answer:

$x = -3$