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Math Help - help with adding and subtracting logarithms

  1. #1
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    help with adding and subtracting logarithms

    I'm having a hard time understanding why the following answer is 2


    I know that log5(20) + log5(10) = log5(200) but I'm not sure how to deal with the -3log5(2) part...

    I get the correct answer with my calculator but can this be solved without a calculator?

    Thanks for the help
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  2. #2
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    Re: help with adding and subtracting logarithms

    Quote Originally Posted by justincase13 View Post
    I'm having a hard time understanding why the following answer is 2


    I know that log5(20) + log5(10) = log5(200) but I'm not sure how to deal with the -3log5(2) part...

    I get the correct answer with my calculator but can this be solved without a calculator?

    Thanks for the help
    Yes, it can be solved quite easily without a calculator. Let's do it step by step.

    $log_5(20) + log_5(10) - 3log_5(2) = log_5(20) + log_5(10) - log_5(2^3) = log_5\left(\dfrac{20 * 10}{2^3}\right) =$

    $log_5\left(\dfrac{200}{8}\right) = log_5(25) = log_5(5^2) = 2log_5(5) = 2 * 1 = 2.$
    Thanks from justincase13
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  3. #3
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    Re: help with adding and subtracting logarithms

    Thank you so much
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