Question

1024^{3x + 3} = 64^{x - 3}

Explanation:

Step1: Express bases as powers of 2

$1024=2^{10}$, $64=2^6$, so substitute:
$2^{10(3x+3)} = 2^{6(x-3)}$

Step2: Set exponents equal (same base)

Since $a^m=a^n \implies m=n$:
$10(3x+3) = 6(x-3)$

Step3: Expand both sides

$30x + 30 = 6x - 18$

Step4: Isolate x terms

Subtract $6x$ and $30$:
$30x - 6x = -18 - 30$
$24x = -48$

Step5: Solve for x

Divide by 24:
$x = \frac{-48}{24}$

Answer:

$x = -2$