8log2 - 6log216 + 81log3 - 5log akar 3 dari 625
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- ![^{5} log \sqrt[3]{625}](https://tex.z-dn.net/?f=%5E%7B5%7D+log+%5Csqrt%5B3%5D%7B625%7D "^{5} log \sqrt[3]{625}")
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IcukSugiarto
![~^{8}log\ 2-~^{6}log\ 216+~^{81}log\ 3-~^{5}log\ \sqrt[3]{625}\\\\\boxed{=~^{2^{3}}log\ 2-~^{6}log\ 6^{3}+~^{3^{4}}log\ 3-~^{5}log\ 625^{ \frac{1}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3-~^{5}log\ (5^{4})^{ \frac{1}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3-~^{5}log\ (5)^{ \frac{4}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3- \frac{4}{3} ~^{5}log\ 5}](https://tex.z-dn.net/?f=%7E%5E%7B8%7Dlog%5C+2-%7E%5E%7B6%7Dlog%5C+216%2B%7E%5E%7B81%7Dlog%5C+3-%7E%5E%7B5%7Dlog%5C++%5Csqrt%5B3%5D%7B625%7D%5C%5C%5C%5C%5Cboxed%7B%3D%7E%5E%7B2%5E%7B3%7D%7Dlog%5C+2-%7E%5E%7B6%7Dlog%5C+6%5E%7B3%7D%2B%7E%5E%7B3%5E%7B4%7D%7Dlog%5C+3-%7E%5E%7B5%7Dlog%5C++625%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D%7D%5C%5C%5C%5C%5Cboxed%7B%3D+%5Cfrac%7B1%7D%7B3%7D+%7E%5E%7B2%7Dlog%5C+2-3%7E%5E%7B6%7Dlog%5C+6%2B+%5Cfrac%7B1%7D%7B4%7D+%7E%5E%7B3%7Dlog%5C+3-%7E%5E%7B5%7Dlog%5C++%285%5E%7B4%7D%29%5E%7B+%5Cfrac%7B1%7D%7B3%7D+%7D%7D%5C%5C%5C%5C%5Cboxed%7B%3D+%5Cfrac%7B1%7D%7B3%7D+%7E%5E%7B2%7Dlog%5C+2-3%7E%5E%7B6%7Dlog%5C+6%2B+%5Cfrac%7B1%7D%7B4%7D+%7E%5E%7B3%7Dlog%5C+3-%7E%5E%7B5%7Dlog%5C++%285%29%5E%7B+%5Cfrac%7B4%7D%7B3%7D+%7D%7D%5C%5C%5C%5C%5Cboxed%7B%3D+%5Cfrac%7B1%7D%7B3%7D+%7E%5E%7B2%7Dlog%5C+2-3%7E%5E%7B6%7Dlog%5C+6%2B+%5Cfrac%7B1%7D%7B4%7D+%7E%5E%7B3%7Dlog%5C+3-+%5Cfrac%7B4%7D%7B3%7D+%7E%5E%7B5%7Dlog%5C++5%7D "~^{8}log\ 2-~^{6}log\ 216+~^{81}log\ 3-~^{5}log\ \sqrt[3]{625}\\\\\boxed{=~^{2^{3}}log\ 2-~^{6}log\ 6^{3}+~^{3^{4}}log\ 3-~^{5}log\ 625^{ \frac{1}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3-~^{5}log\ (5^{4})^{ \frac{1}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3-~^{5}log\ (5)^{ \frac{4}{3} }}\\\\\boxed{= \frac{1}{3} ~^{2}log\ 2-3~^{6}log\ 6+ \frac{1}{4} ~^{3}log\ 3- \frac{4}{3} ~^{5}log\ 5}")
![======================================\\\underline{\bold{Note:}}\\\\remember\ this\ formula:\\1]\boxed{~^{a}log\ (b \times c)=~^{a}log\ b+~^{a}log\ c}\\\\2]\boxed{~^{a}log\ b= \frac{1}{~^{b}log\ a} }\\\\3]\boxed{~^{a}log\ a = 1}\\\\4]\boxed{~^{a}log\ b^{m}=m~^{a}log\ b}\\\\5]\boxed{~^{a^{n}}log\ b^{m}= \frac{m}{n} ~^{a}log\ b}\\\\6]\boxed{ \sqrt[n]{a} =a^{ \frac{1}{n} }}](https://tex.z-dn.net/?f=+%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5Cunderline%7B%5Cbold%7BNote%3A%7D%7D%5C%5C%5C%5Cremember%5C+this%5C+formula%3A%5C%5C1%5D%5Cboxed%7B%7E%5E%7Ba%7Dlog%5C+%28b+%5Ctimes+c%29%3D%7E%5E%7Ba%7Dlog%5C+b%2B%7E%5E%7Ba%7Dlog%5C+c%7D%5C%5C%5C%5C2%5D%5Cboxed%7B%7E%5E%7Ba%7Dlog%5C+b%3D+%5Cfrac%7B1%7D%7B%7E%5E%7Bb%7Dlog%5C+a%7D+%7D%5C%5C%5C%5C3%5D%5Cboxed%7B%7E%5E%7Ba%7Dlog%5C+a+%3D+1%7D%5C%5C%5C%5C4%5D%5Cboxed%7B%7E%5E%7Ba%7Dlog%5C+b%5E%7Bm%7D%3Dm%7E%5E%7Ba%7Dlog%5C+b%7D%5C%5C%5C%5C5%5D%5Cboxed%7B%7E%5E%7Ba%5E%7Bn%7D%7Dlog%5C+b%5E%7Bm%7D%3D+%5Cfrac%7Bm%7D%7Bn%7D+%7E%5E%7Ba%7Dlog%5C+b%7D%5C%5C%5C%5C6%5D%5Cboxed%7B+%5Csqrt%5Bn%5D%7Ba%7D+%3Da%5E%7B+%5Cfrac%7B1%7D%7Bn%7D+%7D%7D "======================================\\\underline{\bold{Note:}}\\\\remember\ this\ formula:\\1]\boxed{~^{a}log\ (b \times c)=~^{a}log\ b+~^{a}log\ c}\\\\2]\boxed{~^{a}log\ b= \frac{1}{~^{b}log\ a} }\\\\3]\boxed{~^{a}log\ a = 1}\\\\4]\boxed{~^{a}log\ b^{m}=m~^{a}log\ b}\\\\5]\boxed{~^{a^{n}}log\ b^{m}= \frac{m}{n} ~^{a}log\ b}\\\\6]\boxed{ \sqrt[n]{a} =a^{ \frac{1}{n} }}")
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