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alexeis_nicole

  • 3 years ago

solve \[3^{2x}-5(3^x)=-6\]

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  1. anonymous
    • 3 years ago
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    solve \[u^2-5u+6=0\] by factoring, then replace \(u\) by \(5^x\) and solve for \(x\)

  2. anonymous
    • 3 years ago
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    \[u^2-5u+6=0\] \[(u-2)(u-3)=0\] \[u=2,u=3\] \[5^x=2\iff x=\log_5(2)\] \[5^x=3\iff x=\log_5(3)\]

  3. alexeis_nicole
    • 3 years ago
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    the answer is supposed to be 1 or 0.631

  4. alexeis_nicole
    • 3 years ago
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    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
    • 3 years ago
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    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. alexeis_nicole
    • 3 years ago
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    LOL its okay. thank you for your help

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