Question 236404
Solve for x:
{{{9^(x-1) = (1/3)^(2x)}}} Substitute {{{9 = 3^2}}}
{{{(3^2)^(x-1) = (1/3)^(2x)}}} Multiply the exponents on the left side.
{{{3^(2x-2) = (1/3)^(2x)}}} Invert the right side and change the sign of the exponent.
{{{3^(2x-2) = 3^(-2x)}}} Now since the bases (3) are equal, the exponents must be equal, so...
{{{2x-2 = -2x}}} Add 2x to both sides.
{{{4x-2 = 0}}} Add 2 to both sides.
{{{4x = 2}}} Divide both sides by 4.
{{{x = 2/4}}} Simplify.
{{{highlight(x = 1/2)}}}