Question

solve for x.
$3^{3x + 5} = 81^4$
show your work here

Explanation:

Step1: Rewrite base 81 as power of 3

$81 = 3^4$, so $81^4 = (3^4)^4 = 3^{16}$

Step2: Set exponents equal (same base)

Since $3^{3x+5} = 3^{16}$, we get $3x + 5 = 16$

Step3: Isolate the term with $x$

Subtract 5 from both sides: $3x = 16 - 5 = 11$

Step4: Solve for $x$

Divide by 3: $x = \frac{11}{3}$

Answer:

$x = \frac{11}{3}$