Logarithm Rules – Evaluating Logarithms by Condensing or Expanding

Evaluating Logarithms by Condensing or Expanding

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The problems in this lesson involve evaluating logarithms by condensing or expanding logarithms. For example, to evaluate log base 8 of 16 plus log base 8 of 4, we condense the logarithms into a single logarithm by applying the following rule: log base b of M + log base b of N = log base b of MN. So we have log base 8 of (16)(4), or log base 8 of 64. Next, we set the logarithmic expression equal to x, and we have log base 8 of 64 = x. Finally, we convert the logarithmic expression to exponential form, and we have 8^x = 64, so x = 2. So we've evaluated the logarithm by first condensing logarithms, then setting the condensed logarithm equal to x, then converting it to exponential form. In other examples, we evaluate logarithms by expanding logarithms. No expanding logarithms calculator is required.
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