How do you condense $25 ln 5 - 5 ln 11$ $25ln5-5ln11$ ?

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Answer 1 · 2016-09-18T05:17:52

$ln (\frac{5^{25}}{11^{5}})$ $ln(5^25/11^5)$ .

We know that, $m ln a = {ln a}^{m}, and, ln a - ln b = ln (\frac{a}{b})$ $mlna=lna^m, and, lna-lnb=ln(a/b)$ .

Hence,

$25 ln 5 - 5 ln 11 = {ln 5}^{25} - {ln 11}^{5} = ln (\frac{5^{25}}{11^{5}})$ $25ln5-5ln11=ln5^25 - ln 11^5=ln(5^25/11^5)$ .

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