Question

solve. write your answer as an integer or a fraction in simplest form.
$27^{2x + 2} = 81$
$x = \square$

Explanation:

Step1: Rewrite bases as powers of 3

$27 = 3^3$, $81 = 3^4$, so substitute:
$$(3^3)^{2x+2} = 3^4$$

Step2: Simplify left side exponent

Use exponent rule $(a^m)^n=a^{m \cdot n}$:
$$3^{3(2x+2)} = 3^4$$

Step3: Set exponents equal

Since bases are equal, exponents are equal:
$$3(2x+2) = 4$$

Step4: Expand left side

Distribute the 3:
$$6x + 6 = 4$$

Step5: Isolate the variable term

Subtract 6 from both sides:
$$6x = 4 - 6 = -2$$

Step6: Solve for x

Divide both sides by 6, simplify fraction:
$$x = \frac{-2}{6} = -\frac{1}{3}$$

Answer:

$-\frac{1}{3}$