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anonymous

  • one year ago

What is 27^(2x) = 9^(x-3)

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  1. Caishaax3
    • one year ago
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    do you need x?

  2. anonymous
    • one year ago
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    Yes. Sorry I forgot to write that.

  3. Caishaax3
    • one year ago
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    x=-3/2

  4. jdoe0001
    • one year ago
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    what's \(3^2=?\) and, say what's \(3^3=?\)

  5. anonymous
    • one year ago
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    Can you explain how to get that?

  6. jdoe0001
    • one year ago
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    \(\large { {\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x-3}\qquad \begin{cases} 3^2\to {\color{brown}{ 9}}\\ 3^3\to {\color{brown}{ 27}} \end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x-3} }\) see how to get "x" now?

  7. anonymous
    • one year ago
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    Um...not exactly sure....Am I suppose to combine the 2x and x-3?

  8. jdoe0001
    • one year ago
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    \(\large { {\color{brown}{ 27}}^{2x} = {\color{brown}{ 9}}^{x-3}\qquad \begin{cases} 3^2\to {\color{brown}{ 9}}\\ 3^3\to {\color{brown}{ 27}} \end{cases}\qquad thus\implies (3^3)^{2x}=(3^2)^{x-3} \\ \quad \\ 3^{3\cdot (2x)}=3^{2\cdot (x-3)}\impliedby \begin{array}{llll} \textit{same base, thus}\\\ \textit{exponents must also equal each other} \end{array}\\ \quad \\ 3(2x)=2(x-3) }\)

  9. jdoe0001
    • one year ago
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    \(\large a^{whatever} = a^{whatever}\) means that whatever = whatever

  10. anonymous
    • one year ago
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    Ohh! So then: 6x=2x-6 4x=-6 x=-2/3

  11. anonymous
    • one year ago
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    Is that right?

  12. jdoe0001
    • one year ago
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    yeap

  13. jdoe0001
    • one year ago
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    hmmm actually wait

  14. anonymous
    • one year ago
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    Thanks!

  15. jdoe0001
    • one year ago
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    \(\bf 6x=2x-6\implies 4x=-6\implies x=-\cfrac{\cancel{6}}{\cancel{4}}\implies x=-\cfrac{3}{2}\)

  16. anonymous
    • one year ago
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    Oh whoops! Thanks for catching that!

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