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sammysweets

  • 2 years ago

What is the solution to the equation 9^(x - 2) = 27 ? x = 2.5 x = 0.5 x = -0.5 x = 3.5

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  1. jim_thompson5910
    • 2 years ago
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    Hint: rewrite 9 as 3^2 and 27 as 3^3

  2. jim_thompson5910
    • 2 years ago
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    Then you can say 9^(x - 2) = 27 (3^2)^(x - 2) = 3^3 3^(2(x-2)) = 3^3

  3. sammysweets
    • 2 years ago
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    would the answer be... x=2.5?

  4. jim_thompson5910
    • 2 years ago
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    Check: 9^(x - 2) = 27 9^(2.5 - 2) = 27 ... plug in the *possible* solution x = 2.5 9^(0.5) = 27 3 = 27 The last equation is false, so x = 2.5 is NOT the answer

  5. sammysweets
    • 2 years ago
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    ahh i'm still confused.

  6. jim_thompson5910
    • 2 years ago
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    the bases are the same in 3^(2(x-2)) = 3^3 so the exponents are the same: 2(x-2) = 3

  7. jim_thompson5910
    • 2 years ago
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    what do you get when you solve 2(x-2) = 3

  8. sammysweets
    • 2 years ago
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    0...? i'm sorry. i'm really bad at math.

  9. jim_thompson5910
    • 2 years ago
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    that's ok, you'll get better with practice distribute to get 2(x-2) = 3 2x-4 = 3 what's next?

  10. jasonxx
    • 2 years ago
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    2x=7 x=7/2

  11. sammysweets
    • 2 years ago
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    am i just plugging in the answer choices for x?

  12. jim_thompson5910
    • 2 years ago
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    you can if you want to check (that's what I would do)

  13. jim_thompson5910
    • 2 years ago
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    btw, x = 7/2 is the same as x = 3.5

  14. sammysweets
    • 2 years ago
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    ohhh okay thank you so much.

  15. samantha.m.
    • 5 months ago
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    im so comfused I worked it out like this 9^(x-2)=27 3^2(x-2)=3^9 3^2x-4=3^9 2x-4=9 2x=13 13\2 x=6.5 but its not a choice. I have pluged in all of them and nothing im so condused. if anyone finds an answer please let me know

  16. jim_thompson5910
    • 5 months ago
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    27 is NOT equal to 3^9 you're thinking of 3 times 9 = 27 ------------------------------------------------------- It should be 27 = 3^3

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