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    Algebra Solutions

    Topics || Problems
    Formulas Concerning Logarithms

    Let a, b, n, M, N be positive numbers.

    1. \( \log_a MN = \log_a M + \log_a N\)
    2. \( \log_a \frac{M}{N} = \log_a M -\log_a N\)
    3. \( \ log_a N^n = n \log_a N\)
    4. \( \log_a \sqrt[n]{N} = \frac{1}{n} \log_a N\)
    5. \( \log_a \frac{1}{N} = - \log_a N\)
    6. \( \log_a a = 1\)
    7. \( \log_a 1 = 0\)
    8. \( \log_a 0= -\infty \)
    9. \( \log_b N= ( \log_a N ) ( log_b a) \)
    10. \( \log_b a= \frac{1}{ \log_a b}\)
    11. \( a^{\log_a N}= N \)
    12. \( \log_a M = \frac{ \log M}{log a} \)
    13. \( \log_e M = ln M\)
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