Question 1074918

Please help me solve this question - I've been trying to set the bases equal. I know that the answer is x=3, but I can't quite get there with showing my work.

2*(2^2x)=(4^x)+64

Thank you
<pre>{{{2(2^(2x)) = 4^x + 64}}}
{{{2(2^(2x)) - 4^x = 64}}} ------ Subtracting {{{4^x}}} from each side
{{{2(2^(2x)) - (2^2)^x = 64}}}
{{{2(2^(2x)) - 2^(2x) = 64}}}
{{{2^(2x) = 64}}}
{{{2^(2x) = 2^6}}}
2x = 6 ------- Bases are equal and so are their exponents
{{{highlight_green(matrix(1,5, x, "=", 6/2, "=", 3))}}}