Solve for x (2/3)^(x-2)=8/27

${(\frac{2}{3})}^{x - 2} = \frac{8}{27}$

Create equivalent expressions in the equation that all have equal bases.

${(\frac{2}{3})}^{x - 2} = {(\frac{2}{3})}^{3}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x - 2 = 3$

Move all terms not containing $x$ to the right side of the equation.

Add $2$ to both sides of the equation.

$x = 3 + 2$

Add $3$ and $2$ .

$x = 5$