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Amenah8

  • one year ago

Calculus: rewrite 9^2x, base 3

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  1. phi
    • one year ago
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    can you write 9 as 3 to some power?

  2. Amenah8
    • one year ago
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    3^2

  3. Amenah8
    • one year ago
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    now what do i do?

  4. Amenah8
    • one year ago
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    |dw:1439220479304:dw|

  5. anonymous
    • one year ago
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    Replace 9 by 3^2...

  6. anonymous
    • one year ago
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    |dw:1439220587021:dw|

  7. Amenah8
    • one year ago
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    3^2(2x), base 3?

  8. Amenah8
    • one year ago
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    3^4x?

  9. phi
    • one year ago
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    did we start with \[ 9^{2x} \] ?

  10. anonymous
    • one year ago
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    3^{4x} is good to me..

  11. phi
    • one year ago
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    if so then we replace 9 with 3^2 \[ \left(3^2\right)^{2x} \] and use the rule \[ \left(a^b\right)^c = a^{b\cdot c} \] to get \[ 3^{2\cdot 2\cdot x} = 3^{4x} \]

  12. anonymous
    • one year ago
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    \[(a^m)^n = (a)^{m \times n}\]

  13. Amenah8
    • one year ago
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    so sorry something went wrong with my computer. thanks for staying

  14. Amenah8
    • one year ago
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    ah! okay i'm back now, sorry

  15. Amenah8
    • one year ago
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    so now i have 3^4x, base 3. does the base 3 just mean that, by replacing 9 with 3^2, I got a base of 3? or do i somehow have to apply base 3 to 3^4x?

  16. Vocaloid
    • one year ago
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    yeah, you're done. 3^4x is already in base 3, since 3 is being raised to a power

  17. Amenah8
    • one year ago
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    thanks so much!! this is just a quick question, but what would i do for a problem like this where i have to make a fraction 1/8 with a base of 2?

  18. Vocaloid
    • one year ago
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    similar process, except we're dealing with a negative exponent 1/8 = 1/2^3 = 2^(-3)

  19. Amenah8
    • one year ago
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    how did you know it was 1/2^3?

  20. Vocaloid
    • one year ago
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    8 = 2^3 therefore 1/8 = 1/2^3

  21. Vocaloid
    • one year ago
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    to make a bit more clear 1/8 = 1/(2^3)

  22. Amenah8
    • one year ago
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    i get it! thank you os much!!

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