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Math Help - How do I solve for this exponent using logs?

  1. #1
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    How do I solve for this exponent using logs?

    (4.0)(8.0)^z = (7.0)(3.0)^(z-1)

    I have to solve for z. I'm reviewing basic logarithm rules but I can't remember how to do this at all.

    Can someone provide some insight? Thanks!
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by Jeavus View Post
    (4.0)(8.0)^z = (7.0)(3.0)^(z-1)

    I have to solve for z. I'm reviewing basic logarithm rules but I can't remember how to do this at all.

    Can someone provide some insight? Thanks!
    Just use the following rules :

    \log(ab)=\log(a)+\log(b)

    \log(a^b)=b \log(a)
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  3. #3
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    Do I have to take the log of just the (8.0)^z and the (3.0)^(z-1)? Or the entire term itself? That's where I'm having trouble...
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  4. #4
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    Quote Originally Posted by Jeavus View Post
    Do I have to take the log of just the (8.0)^z and the (3.0)^(z-1)? Or the entire term itself? That's where I'm having trouble...
    a=b \Longleftrightarrow \log(a)=\log(b) (a and b positive)

    So \log(4 \cdot 8^z)=\log(7 \cdot 3^{z-1})
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  5. #5
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    Thanks! I got it!
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