Logarithm Properties

Mrs Lenox Math Help: Logarithms

Add and Multiply

Properties

To expand the logarithm (break it apart),rewrite multiplication as the same base logarithm being added.

log35x = log35 + log3x

To simplify the logarithm(put it together), if the logarithms have the same base, keep the logarithm and base, and multiply the arguments together.

log102 + log107 = log10(2x7) = log1014

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Subtract and Divide

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To expand the logarithm (break it apart),rewrite division as the same base logarithm being subtracted.

log35/x = log35 - log3x

To simplify the logarithm(put it together), if the logarithms have the same base, keep the logarithm and base, and divide the arguments.

log1012 - log103 = log10(12/3) = log104

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Multiply and Powers

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To expand the logarithm (break it apart),rewrite exponents as factors in front of the logarithm.

log35x = xlog35

To simplify the logarithm(put it together), if there is a factor out front, make it the exponent of the argument.

2log53=log532 =log59

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Rewrite Logs as Exponential

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To convert the logarithm to exponential form,drop the word log, and switch the numbers surrounding the equal sign.

Logarithms

To convert exponential form to logarithmic, add the word log and swap the two numbers surrounding the equal sign.

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Change of Base

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To change the base of a logarithm, choose your new base (10,so you can use the calculator,for example), and write the word log and your base twice as a fraction. The original base goes on the bottom and the original argument on the top.

Logarithms

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Practice Problems

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