Question 210168
Solve:
{{{8^x^2 = 2^((x+4))}}} Substitute {{{8 = 2^3}}}
{{{(2^3)^x^2 = 2^((x+4))}}} Simplify the left side.
{{{2^(3x^2) = 2^((x+4))}}} Now since the bases are equal (2) the exponents are equal,so...
{{{3x^2 = x+4}}} Subtract (x+4) from both sides.
{{{3x^3-x-4 = 0}}} Factor this trinomial.
{{{(3x-4)(x+1) = 0}}} Apply the zero product rule.
{{{3x-4 = 0}}} or {{{x+1 = 0}}} which means that...
{{{3x = 4}}} and {{{highlight(x = 4/3)}}} or {{{highlight(x = -1)}}}