Question

question
solve for x:
$4^{-x - 5} = 64^{-x - 7}$
answer
attempt 2 out of 2

Explanation:

Step1: Rewrite base 64 as power of 4

$64 = 4^3$, so substitute into equation:
$4^{-x-5} = (4^3)^{-x-7}$

Step2: Simplify right-hand side

Use exponent rule $(a^m)^n = a^{m \cdot n}$:
$4^{-x-5} = 4^{3(-x-7)}$
$4^{-x-5} = 4^{-3x-21}$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$-x - 5 = -3x - 21$

Step4: Solve for x

Add $3x$ to both sides:
$2x - 5 = -21$
Add 5 to both sides:
$2x = -16$
Divide by 2:
$x = \frac{-16}{2}$

Answer:

$x = -8$