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Math Help - Simplify logs

  1. #1
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    Simplify logs

    Help needed with this question:

    Log10(B^3) - (Log10(AB)-Log10(A/B))
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  2. #2
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    Quote Originally Posted by oldskool_89 View Post
    Help needed with this question:

    Log10(B^3) - (Log10(AB)-Log10(A/B))
    Familiar with logarithmic properties?

    The Four Basic Properties of Logs

    1. log(xy) = log(x) + log(y)
    2. log(x/y) = log(x) - log(y)
    3. log(xn) = n log(x)
    4. log(x) = log(x) / log(b)

    \log(b^3) - \log(ab) + \log(\frac{a}{b})

    3\log(b) - \log(a) - \log(b) + \log(a) - \log(b)

    \log(b)
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  3. #3
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    Quote Originally Posted by oldskool_89 View Post
    Help needed with this question:

    Log10(B^3) - (Log10(AB)-Log10(A/B))
    log10(AB) - log10(A/B) = log10(B^3)

    B^3 = AB / (A/B) = AB * B/A = AB^2/A = B^2

    B^3 - B^2 = 0

    B^2(B - 1) = 0

    Either B = 0 or B = 1
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  4. #4
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    Hello, oldskool_89!

    There are number of ways to simplify this . . .


    \log(B^3) - \bigg[\log(AB)- \log\left(\frac{A}{B}\right)\bigg]
    We have: . \log(B^3) - \log(AB) + \log\left(\frac{A}{B}\right) \;= \;\log\left(\frac{B^3}{AB}\cdot\frac{A}{B}\right) \;=\;\log(B)

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