Question

solve $3^{2x + 10} = 81^{x}$
select one:
a. $x = -10$
b. $x = -3$
c. $x = 5$
d. $x = -5$

Explanation:

Step1: Rewrite 81 as power of 3

$81 = 3^4$, so $81^x = (3^4)^x = 3^{4x}$

Step2: Set exponents equal (same base)

Since $3^{2x+10} = 3^{4x}$, equate exponents:
$2x + 10 = 4x$

Step3: Solve for x

Subtract $2x$ from both sides:
$10 = 2x$
Divide by 2:
$x = 5$

Answer:

C. $x = 5$