Question

question
solve for x:
$6^{2x + 5} = 216^{x - 4}$

Explanation:

Step1: Rewrite base to match

$216 = 6^3$, so substitute:
$6^{2x+5} = (6^3)^{x-4}$

Step2: Simplify right-hand exponent

Use exponent rule $(a^m)^n = a^{mn}$:
$6^{2x+5} = 6^{3(x-4)}$
$6^{2x+5} = 6^{3x-12}$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$2x + 5 = 3x - 12$

Step4: Solve for x

Subtract $2x$ and add 12 to both sides:
$5 + 12 = 3x - 2x$
$17 = x$

Answer:

$x = 17$