Question 29309
Solve for x: All logs are to the base 10.
{{{log(8)-(1/3)log(x) = log(2)}}} Add{{{(1/3)log(x)}}} to both sides of the equation.
{{{log(8) = (1/3)log(x) + log(2)}}} Subtract {{{log(2)}}} from both sides.
{{{log(8)-log(2) = (1/3)log(x)}}} Apply the "quotient rule" for logarithms to the left side.
{{{log(8/4) = (1/3)log(x)}}}
{{{log(4) = (1/3)log(x)}}} Multiply both sides by 3.
{{{3log(4) = log(x)}}}
{{{log(4^3) = log(x)}}}
{{{4^3 = x}}}
{{{x = 64}}}