Log_{ \frac{1}{2}}5* log_{5}16=
log_{5}8-log{5} 1000 =
log_{12}4+ log_{12}36=
log9+2log\frac{1}{3}=
log_{3}\sqrt[4]{27} =
log_{5}8-log{5} 1000 =
log_{12}4+ log_{12}36=
log9+2log\frac{1}{3}=
log_{3}\sqrt[4]{27} =
animaldk
![log_\frac{1}{2}5\cdot log_516=\frac{1}{log_5\frac{1}{2}}\cdot log_516=\frac{log_52^4}{\log_52^{-1}}=\frac{4log_52}{-log_52}=-4\\\\log_58-log_51000=log_5\frac{8}{1000}=log_5\frac{1}{125}=log_55^{-3}=-3log_55=-3\\\\log_{12}4+log_{12}36=log_{12}(4\cdot36)=log_{12}144=log_{12}12^2=2log_{12}12=2\\\\log9+2log\frac{1}{3}=log9+log(\frac{1}{3})^2=log9+log\frac{1}{9}=log(9\cdot\frac{1}{9})=log1=0\\\\log_3\sqrt[4]{27}=log_3\sqrt[4]{3^3}=log_33^\frac{3}{4}=\frac{3}{4}log_33=\frac{3}{4}](https://tex.z-dn.net/?f=log_%5Cfrac%7B1%7D%7B2%7D5%5Ccdot+log_516%3D%5Cfrac%7B1%7D%7Blog_5%5Cfrac%7B1%7D%7B2%7D%7D%5Ccdot+log_516%3D%5Cfrac%7Blog_52%5E4%7D%7B%5Clog_52%5E%7B-1%7D%7D%3D%5Cfrac%7B4log_52%7D%7B-log_52%7D%3D-4%5C%5C%5C%5Clog_58-log_51000%3Dlog_5%5Cfrac%7B8%7D%7B1000%7D%3Dlog_5%5Cfrac%7B1%7D%7B125%7D%3Dlog_55%5E%7B-3%7D%3D-3log_55%3D-3%5C%5C%5C%5Clog_%7B12%7D4%2Blog_%7B12%7D36%3Dlog_%7B12%7D%284%5Ccdot36%29%3Dlog_%7B12%7D144%3Dlog_%7B12%7D12%5E2%3D2log_%7B12%7D12%3D2%5C%5C%5C%5Clog9%2B2log%5Cfrac%7B1%7D%7B3%7D%3Dlog9%2Blog%28%5Cfrac%7B1%7D%7B3%7D%29%5E2%3Dlog9%2Blog%5Cfrac%7B1%7D%7B9%7D%3Dlog%289%5Ccdot%5Cfrac%7B1%7D%7B9%7D%29%3Dlog1%3D0%5C%5C%5C%5Clog_3%5Csqrt%5B4%5D%7B27%7D%3Dlog_3%5Csqrt%5B4%5D%7B3%5E3%7D%3Dlog_33%5E%5Cfrac%7B3%7D%7B4%7D%3D%5Cfrac%7B3%7D%7B4%7Dlog_33%3D%5Cfrac%7B3%7D%7B4%7D "log_\frac{1}{2}5\cdot log_516=\frac{1}{log_5\frac{1}{2}}\cdot log_516=\frac{log_52^4}{\log_52^{-1}}=\frac{4log_52}{-log_52}=-4\\\\log_58-log_51000=log_5\frac{8}{1000}=log_5\frac{1}{125}=log_55^{-3}=-3log_55=-3\\\\log_{12}4+log_{12}36=log_{12}(4\cdot36)=log_{12}144=log_{12}12^2=2log_{12}12=2\\\\log9+2log\frac{1}{3}=log9+log(\frac{1}{3})^2=log9+log\frac{1}{9}=log(9\cdot\frac{1}{9})=log1=0\\\\log_3\sqrt[4]{27}=log_3\sqrt[4]{3^3}=log_33^\frac{3}{4}=\frac{3}{4}log_33=\frac{3}{4}")
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Miisiek99
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