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How do I solve this log problem step by step?

log problem

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I have been struggling with how to show my work on this.

thank you

Margaret

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    Hi, welcome to Math.SE. Please indicate what you have tried, your thoughts on the problem and where you got stuck. This will help people better tailor their answer to your background and situation. It will also demonstrate that you are interested in your question and not just looking for someone to do your homework for you - Math.SE is not a homework site. – 2017-01-22
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    Additionally using the word "solve" here doesn't make sense. Are you trying to evaluate it? Please expand upon this question lots. – 2017-01-22

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We know $\log_{b} a =\frac {\log a}{\log b} $ and that $\log ab = \log a +\log b $. Now we thus get, $$14\log_{14}(6) = 14\frac{\log 6}{\log 14} =14\frac {\log 2 +\log 3}{\log 2 +\log 7} $$ Hope it helps.

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    I don't see how this answer simplifies the given expression in any manner. The result still includes a $\log$ value which requires using a calculator. In fact, it includes more than one such value, in opposed to the original expression. So if anything, it complicates the given expression. Having said that, since this answer was down-voted without any comment explaining why, I am up-voting it in order to "make it even". IMO, if there is something wrong with an answer, then the down-voter should bother to explain it. Otherwise, this act is pure trolling. – 2017-01-22
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    Rohan, thank you for explaining that. It pointed me in the right direction. Best regards. – 2017-01-25
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    Welcome @nickp. Happy it helped. – 2017-01-25