Jika 
log x =2 , log y = 3 , log z = 4 , tentukan
![^{a}log ( \frac{ \sqrt[3]{ x^{2} z} }{ \sqrt[3]{ y^{2} z^{-2} } } )=](https://tex.z-dn.net/?f=+%5E%7Ba%7Dlog+%28+%5Cfrac%7B+%5Csqrt%5B3%5D%7B+x%5E%7B2%7D+z%7D+%7D%7B+%5Csqrt%5B3%5D%7B+y%5E%7B2%7D+z%5E%7B-2%7D+%7D+%7D+%29%3D "^{a}log ( \frac{ \sqrt[3]{ x^{2} z} }{ \sqrt[3]{ y^{2} z^{-2} } } )=")
ibnnurjen
![^alog \frac{ \sqrt[3]{x^2z} }{ \sqrt[3]{y^2z^{-2}} } \\ =^alog \frac{ x^ \frac{2}{3}.z^ \frac{1}{3} }{ y^ \frac{2}{3}.z^ {-\frac{2}{3}} } \\ =^alog \frac{ x^ \frac{2}{3}.z^{ \frac{1}{3} - (-\frac{2}{3})} }{ y^ \frac{2}{3} } \\ =^alog \frac{ x^ \frac{2}{3}.z^{ \frac{1}{3} +\frac{2}{3}} }{ y^ \frac{2}{3} } \\ =^alog \frac{ x^ \frac{2}{3}.z }{ y^ \frac{2}{3} } \\ =^alogx^ \frac{2}{3}+^alogz-^alogy^ \frac{2}{3} \\ =\frac{2}{3}.^alogx+^alogz- \frac{2}{3}.^alogy](https://tex.z-dn.net/?f=%5Ealog+%5Cfrac%7B+%5Csqrt%5B3%5D%7Bx%5E2z%7D+%7D%7B+%5Csqrt%5B3%5D%7By%5E2z%5E%7B-2%7D%7D+%7D++%5C%5C+%3D%5Ealog+%5Cfrac%7B+x%5E+%5Cfrac%7B2%7D%7B3%7D.z%5E+%5Cfrac%7B1%7D%7B3%7D++%7D%7B+y%5E+%5Cfrac%7B2%7D%7B3%7D.z%5E+%7B-%5Cfrac%7B2%7D%7B3%7D%7D+++%7D+%5C%5C+%3D%5Ealog+%5Cfrac%7B+x%5E+%5Cfrac%7B2%7D%7B3%7D.z%5E%7B+%5Cfrac%7B1%7D%7B3%7D+-+%28-%5Cfrac%7B2%7D%7B3%7D%29%7D++%7D%7B+y%5E+%5Cfrac%7B2%7D%7B3%7D++%7D+%5C%5C+%3D%5Ealog+%5Cfrac%7B+x%5E+%5Cfrac%7B2%7D%7B3%7D.z%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%2B%5Cfrac%7B2%7D%7B3%7D%7D++%7D%7B+y%5E+%5Cfrac%7B2%7D%7B3%7D++%7D++%5C%5C+%3D%5Ealog+%5Cfrac%7B+x%5E+%5Cfrac%7B2%7D%7B3%7D.z+%7D%7B+y%5E+%5Cfrac%7B2%7D%7B3%7D++%7D+%5C%5C+%3D%5Ealogx%5E+%5Cfrac%7B2%7D%7B3%7D%2B%5Ealogz-%5Ealogy%5E+%5Cfrac%7B2%7D%7B3%7D+++%5C%5C++%3D%5Cfrac%7B2%7D%7B3%7D.%5Ealogx%2B%5Ealogz-+%5Cfrac%7B2%7D%7B3%7D.%5Ealogy+++ "^alog \frac{ \sqrt[3]{x^2z} }{ \sqrt[3]{y^2z^{-2}} } \\ =^alog \frac{ x^ \frac{2}{3}.z^ \frac{1}{3} }{ y^ \frac{2}{3}.z^ {-\frac{2}{3}} } \\ =^alog \frac{ x^ \frac{2}{3}.z^{ \frac{1}{3} - (-\frac{2}{3})} }{ y^ \frac{2}{3} } \\ =^alog \frac{ x^ \frac{2}{3}.z^{ \frac{1}{3} +\frac{2}{3}} }{ y^ \frac{2}{3} } \\ =^alog \frac{ x^ \frac{2}{3}.z }{ y^ \frac{2}{3} } \\ =^alogx^ \frac{2}{3}+^alogz-^alogy^ \frac{2}{3} \\ =\frac{2}{3}.^alogx+^alogz- \frac{2}{3}.^alogy")
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Ridafahmi
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