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Math Help - Logarithmic

  1. #1
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    Logarithmic

    I have a calc final tomorrow and I can't seem to figure this problem out. Please help. He gave us the answer which was 1.500, but I don't know how he got it.
    Let logb A = 5 and logb B = -2. Find logb 2√AB.






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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by aphan19 View Post
    I have a calc final tomorrow and I can't seem to figure this problem out. Please help. He gave us the answer which was 1.500, but I don't know how he got it.
    Let logb A = 5 and logb B = -2. Find logb 2√AB.





    \log_b(2\sqrt{AB})=\log_b(2)+\log_b(\sqrt{AB})= \log_b(2)+\frac{1}{2}\log_b(AB)=\log_b(2)+\frac{1}  {2}\bigg[\log_b(A)+\log_b(B)\bigg]

    Can you take it from there?
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  3. #3
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    Quote Originally Posted by Mathstud28 View Post
    \log_b(2\sqrt{AB})=\log_b(2)+\log_b(\sqrt{AB})= \log_b(2)+\frac{1}{2}\log_b(AB)=\log_b(2)+\frac{1}  {2}\bigg[\log_b(A)+\log_b(B)\bigg]

    Can you take it from there?
    Yes, I think I can take it from there, but did you get the 1/2 from the square root?
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  4. #4
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    \sqrt{a} = a^{\frac{1}{2}}
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  5. #5
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    I'm stuck on logb (2). When I add it to the rest of the problem it came out to be a completely different answer.
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by aphan19 View Post
    I'm stuck on logb (2). When I add it to the rest of the problem it came out to be a completely different answer.
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    I dont think that two should be there

    Because if it wasnt you would just ahve \frac{1}{2}\bigg[\log_b(A)+\log_b(B)\bigg]=\frac{1}{2}\bigg[5+-2\bigg]=\frac{1}{2}\cdot{3}=\frac{3}{2}=1.5
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