Question

question
solve for x:
$6^{3x - 4} = 1296^{-4}$
answer attempt 1 out of 2
$x = \square$

Explanation:

Step1: Rewrite 1296 as power of 6

$1296 = 6^4$, so $1296^{-4} = (6^4)^{-4}$

Step2: Simplify right-hand side

Using exponent rule $(a^m)^n = a^{mn}$:
$(6^4)^{-4} = 6^{4\times(-4)} = 6^{-16}$

Step3: Set exponents equal

Since bases are equal, $3x - 4 = -16$

Step4: Solve for x

Add 4 to both sides:
$3x = -16 + 4 = -12$
Divide by 3:
$x = \frac{-12}{3} = -4$

Answer:

$x = -4$