Question

1024^x = 64^(2x - 3)

Explanation:

Step1: Rewrite bases as powers of 2

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

Step2: Set exponents equal (same base)

Since $a^m=a^n \implies m=n$ for $a>0,a
eq1$:
$10x = 6(2x-3)$

Step3: Expand right-hand side

$10x = 12x - 18$

Step4: Isolate x terms

Subtract $10x$ and add 18:
$18 = 12x - 10x$

Step5: Simplify and solve for x

$18=2x \implies x=\frac{18}{2}$

Answer:

$x=9$