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Evaluating logarithms using change-of-base formula

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Now Playing:Evaluate logarithms using change of base formula– Example 1
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  1. How to apply ‘‘ `` change-of-base rule""

    Express log⁡53 \log_53 in three different ways.

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    Evaluate Logarithms Using Change Of Base Formula 1
    Evaluating logarithms using change-of-base formula
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    Notes
    • change-of-base rule:
    log⁡ba=log⁡xalog⁡xb=log⁡alog⁡b \log_ba = \frac{\log_xa}{\log_xb} = \frac{\log a}{\log b}

    • common logarithms:
    log with base ‘‘10" ``10"
    example: log⁡3=log⁡103 \log3 = \log_{10}3
    example: log⁡x=log⁡10x \log x = \log_{10}x