Logarithmical equation with addition of powers

Question

I just wonder how to solve the equation: $$ 3^x + 3 \times 9^x = 1200 $$

Mi first idea was to replace $ 9^x $ with $ 3^{2x} $. Then I can mutliply the powers: $$ 3^x + 3^{2x+1}= 1200 $$ But how to go on?

$9^x=(3^x)^2$. Think of quadratic equations. – David Mitra Jan 11 '14 at 22:17 — David Mitra, Jan 11 '14 at 22:17

score 1 · Accepted Answer · edited Jan 11 '14 at 22:25

1

Just substitute: $$z=3^x \implies z+3*z^2=1200$$

edited Jan 11 '14 at 22:25

answered Jan 11 '14 at 22:18

Alex

1 Answers1