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L.H.S.=
![log( \sqrt[3]{6 \frac{2}{9} } ) \\ \\ = log( \frac{56}{9} ) {}^{ \frac{1}{3} } \\ \\ = \frac{1}{3} log( \frac{56}{9} ) \\ \\ = \frac{1}{3} ( log(56) - log(9) ) \\ \\ = \frac{1}{3} log(56) - \frac{1}{3} log(9) \\ \\ = \frac{1}{3} ( log(8 \times 7) - \frac{1}{3} log(3 ) {}^{2} \\ \\ = \frac{1}{3} log(8) + \frac{1}{3} log(7) - \frac{2}{3} log(3) \\ \\ = \frac{1}{3} log(2) {}^{3} + \frac{1}{3} log(7) - \frac{2}{3} log(3) \\ \\ = \frac{3}{3} log(2) + \frac{1}{3} ( log(7) -2 log(3) ) \\ \\ = \frac{1}{3} ( log(7) - 2 log(3) ) + log(2)](https://tex.z-dn.net/?f=+log%28+%5Csqrt%5B3%5D%7B6+%5Cfrac%7B2%7D%7B9%7D+%7D+%29++%5C%5C++%5C%5C++%3D++log%28+%5Cfrac%7B56%7D%7B9%7D+%29++%7B%7D%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D++%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D++log%28+%5Cfrac%7B56%7D%7B9%7D+%29++%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D+%28+log%2856%29++-++log%289%29+%29+%5C%5C++%5C%5C+%3D+++%5Cfrac%7B1%7D%7B3%7D++log%2856%29++-++%5Cfrac%7B1%7D%7B3%7D++log%289%29++%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D+%28+log%288+%5Ctimes+7%29++-++%5Cfrac%7B1%7D%7B3%7D++log%283+%29++%7B%7D%5E%7B2%7D++%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D++log%288%29++%2B++%5Cfrac%7B1%7D%7B3%7D++log%287%29++-++%5Cfrac%7B2%7D%7B3%7D++log%283%29++%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D++log%282%29++%7B%7D%5E%7B3%7D++%2B++%5Cfrac%7B1%7D%7B3%7D++log%287%29++-++%5Cfrac%7B2%7D%7B3%7D++log%283%29++%5C%5C++%5C%5C++%3D++%5Cfrac%7B3%7D%7B3%7D++log%282%29++%2B++%5Cfrac%7B1%7D%7B3%7D+%28+log%287%29++-2++log%283%29+%29+%5C%5C++%5C%5C++%3D++%5Cfrac%7B1%7D%7B3%7D+%28+log%287%29++-+2+log%283%29+%29+%2B++log%282%29+ "log( \sqrt[3]{6 \frac{2}{9} } ) \\ \\ = log( \frac{56}{9} ) {}^{ \frac{1}{3} } \\ \\ = \frac{1}{3} log( \frac{56}{9} ) \\ \\ = \frac{1}{3} ( log(56) - log(9) ) \\ \\ = \frac{1}{3} log(56) - \frac{1}{3} log(9) \\ \\ = \frac{1}{3} ( log(8 \times 7) - \frac{1}{3} log(3 ) {}^{2} \\ \\ = \frac{1}{3} log(8) + \frac{1}{3} log(7) - \frac{2}{3} log(3) \\ \\ = \frac{1}{3} log(2) {}^{3} + \frac{1}{3} log(7) - \frac{2}{3} log(3) \\ \\ = \frac{3}{3} log(2) + \frac{1}{3} ( log(7) -2 log(3) ) \\ \\ = \frac{1}{3} ( log(7) - 2 log(3) ) + log(2)")
= R. H. S.
hope it helps...
= R. H. S.
hope it helps...
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