Question

$36^{x+1}=1296^{x-4}$

Explanation:

Step1: Express bases as powers of 36

Note that $1296 = 36^2$, so rewrite the equation:
$36^{x+1} = (36^2)^{x-4}$

Step2: Simplify the right-hand side

Use exponent rule $(a^m)^n = a^{mn}$:
$36^{x+1} = 36^{2(x-4)}$

Step3: Set exponents equal (same base)

Since bases are equal, exponents must be equal:
$x+1 = 2(x-4)$

Step4: Expand and solve for x

Expand the right-hand side, then isolate x:
$x+1 = 2x - 8$
$1 + 8 = 2x - x$

Answer:

$x=9$