Question 16657
{{{(3^(2x)) + (3^(x+1)) - 4 = 0}}}
{{{3^(2x) + 3^x*3^1 - 4 = 0}}}
{{{3^(2x) + 3^x*3 - 4 = 0}}}
Suppose: {{{p=3^x}}}, so that:
{{{p^2+p*3-4=0}}}
{{{p^2+3p-4=0}}}
(p+4)(p-1)=0
p+4=0 or p-1=0
p=-4 or p=1
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substitute p=-4 to {{{p=3^x}}}:
{{{p=3^x}}}
{{{-4=3^x}}} ------>There is no solution for x
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Substitute p=1 to {{{p=3^x}}}:
{{{p=3^x}}}
{{{1=3^x}}}
{{{3^0=3^x}}}
x=0
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Thus, solution for this problem is x = 0