Evaluate a log please

label Algebra
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Use the Change of Base Formula to evaluate log3 48. Then convert log3 48 to a logarithm in base 5. Round to the nearest thousandth.

May 16th, 2015

So the change of base formula is basically you can replace the original base by another and by creating a fraction. It looks like log base a of b can become (log base x of b)/(log base x of a). Usually x will be 10 because then we can use a calculator to get the exact value. So log base 3 of 48 becomes (log 48)/(log 3). This in the calculator becomes about 3.524 (rounded to thousandth. The next question asks to convert to base five. The way we do this is simply change the base to 5 in the formula. So log base 3 of 48 becomes (log base 5 of 48)/(log base 5 of 3) which simplifies to log5 290.385. Hope this helps

May 16th, 2015

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May 16th, 2015
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May 16th, 2015
Sep 25th, 2017
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