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anonymous 3 years ago solve $3^{2x}-5(3^x)=-6$

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1. anonymous

solve $u^2-5u+6=0$ by factoring, then replace $$u$$ by $$5^x$$ and solve for $$x$$

2. anonymous

$u^2-5u+6=0$ $(u-2)(u-3)=0$ $u=2,u=3$ $5^x=2\iff x=\log_5(2)$ $5^x=3\iff x=\log_5(3)$

3. anonymous

the answer is supposed to be 1 or 0.631

4. anonymous

when i got (u-2)(u-3)=0 i did u=2, u=3 $3^x=3,3^x=2$$x=1,x=\log(2)/\log(3)$

5. anonymous

well i am an idiot, it said $$3^x$$ not $$5^x$$ so i screwed up it should be $$3^x=3$$ so $$x=1$$ or $3^x=2$ so $$x=\frac{\ln(2)}{\ln(3)}$$

6. anonymous

LOL its okay. thank you for your help

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