Question 983082

{{{e^(0.4x) = 4^(x-2)}}}

{{{e^(0.4x) = (2^2)^(x-2)}}}

{{{e^0.4x = 2^(2x-4)}}}

{{{log(e^(0.4x)) = log(2^(2x-4))}}}

{{{(0.4x)log(e) = (2x-4)log(2)}}}....since {{{log(e)=1}}}, we have


{{{0.4x=(2x-4)log(2)}}}

{{{0.4x = 2x*log(2)-4log(2)}}}

{{{4log(2) = 2x*log(2)- 0.4x}}}

{{{4log(2) = 2x(log(2)- 0.2)}}}

{{{2log(2) = x(log(2)- 0.2)}}}

{{{x=2log(2)/(log(2)- 0.2)}}}

{{{x=2.81112}}}