How can we solve an equation like this:
$$3^{2x+1} +9= 3^{x+3} +3^x$$
i.e $3$ raised to the power $2x+2$ plus $9$ equals $3$ raised to the power $x+3$, plus $3$ raised to the power $x$.
2026-03-30 20:47:26.1774903646
Solving complex Exponential equations problem
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Collect all terms on one side, you get $$ 0 = 3^{2x+1} +9 - 3^{x+3} +3^x = 3 \cdot \left(3^x\right)^2 + 9 - 3^3 3^x + 3^x = 3u^2+9-27u+u, $$ where $u=3^x$. Can you finish?