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anonymous

  • 5 years ago

I have the problem 27^4z=9^(z+1) I don't want the answer, just help figuring out the proper way to simplify both sides of the equation so I can add the exponents. I know the bases will be the same, 3^(whatever power)

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  1. anonymous
    • 5 years ago
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    I have gotten as far as 3^3(4z)=3^2(z+1)

  2. amistre64
    • 5 years ago
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    log both sides

  3. anonymous
    • 5 years ago
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    I don't know what to do with the exponents, whether I should add them, multiply them, divide them or whatever else. I am not familiar with the log function yet. The chapter the homework is in is on exponential functions, so trying to do it that way first.

  4. amistre64
    • 5 years ago
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    27^4z=9^(z+1) log(27^4z) = log(9^(z+1)) 4z (log(27)) = (z+1) (log(9)) get like terms together now

  5. anonymous
    • 5 years ago
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    I already have the bases, I just need to know what to do with the exponents. Again, trying to do this without a calculator. I want to understand the process before I rely on a calculator for the answers

  6. amistre64
    • 5 years ago
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    exponents an logs are hand in hand. they are inverses of each other and you need logs to work exponents with a variable in them

  7. amistre64
    • 5 years ago
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    you can "remember" exponents if you want and try to recall what is what... but it is harder

  8. anonymous
    • 5 years ago
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    4z (log(27)) = (z+1) (log(9)) 4z.3log (3)= (z+1)2log (3) 12z=2z+2 z=1/5

  9. amistre64
    • 5 years ago
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    the relation is this: B^x = y x = logB(y)

  10. amistre64
    • 5 years ago
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    3^2 = 9 2 = log3(9)

  11. amistre64
    • 5 years ago
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    As for exponent rules: 3^(2^x) = 3^(2x). when exponents have an exponent; the exponents multiply together

  12. anonymous
    • 5 years ago
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    THAT is what I needed :D The exponent rule.

  13. anonymous
    • 5 years ago
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    I got it right easily that time. Just didn't know what to do with it, thank you very much d:D

  14. amistre64
    • 5 years ago
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    :)

  15. anonymous
    • 5 years ago
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    {I have gotten as far as 3^3(4z)=3^2(z+1)}. when you got this , why are you mess with log.. just compare exponents of 3 n get the result

  16. amistre64
    • 5 years ago
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    easy when you can "know" the base..

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