Question

solve. write your answer as an integer or a fraction in simplest form.
$27^{x}=9$
$x = \square$

Explanation:

Step1: Rewrite bases as powers of 3

$27 = 3^3$, $9 = 3^2$, so substitute:
$$(3^3)^x = 3^2$$

Step2: Simplify left exponent

Use exponent rule $(a^m)^n=a^{mn}$:
$$3^{3x} = 3^2$$

Step3: Set exponents equal

If $a^m=a^n$ ($a
eq1,0$), $m=n$:
$$3x = 2$$

Step4: Solve for x

Divide both sides by 3:
$$x = \frac{2}{3}$$

Answer:

$\frac{2}{3}$