Question

$6^{2x+5} = 216^{x-4}$

Explanation:

Step1: Rewrite 216 as power of 6

$216 = 6^3$, so $216^{x-4} = (6^3)^{x-4}$

Step2: Simplify right-hand side

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

Step3: Set exponents equal (same base)

Since $6^{2x+5} = 6^{3x-12}$, equate exponents:
$2x + 5 = 3x - 12$

Step4: Solve for x

Subtract $2x$ from both sides:
$5 = x - 12$
Add 12 to both sides:
$x = 5 + 12$

Answer:

$x = 17$