Question 1114887
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{{{ (2*4^(x^2-3x))^2= 2^(x-1)}}}<br>
Rewrite every factor as a power of 2; then equate the exponents.<br>
{{{(2*(2^2)^(x^2-3x))^2 = 2^(x-1)}}}
{{{(2^2)*2^(4x^2-12x) = 2^(x-1)}}}
{{{2^(4x^2-12x+2) = 2^(x-1)}}}
{{{4x^2-12x+2 = x-1}}}
{{{4x^2-13x+3 = 0}}}
{{{(4x-1)(x-3) = 0}}}
{{{x = 1/4}}} or {{{x = 3}}}<br>
Answers: x=1/4 and x=3