Question 434121
To solve the equation:{{{5*2^x=3-2^(x+2)}}}, we substitute {{{2^x=y}}} and

{{{2^(x+2)=2^2*2^x=4*y}}}. Rewrite the equation: 5y=3-4y, solve this equation,

5y+4y=3 => 9y=3 => y=1/3. Now we find the x, since 2^x=y, substitute:

{{{2^x=1/3}}}, taking natural logarithms of each side we have:

{{{x*ln2=-ln3}}} => {{{x=-ln3/ln2}}}.

Done.