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4.
![( sqrt[3]{2} )^{3+log_{ frac{1}{2} }3}=( sqrt[3]{2} )^3*( sqrt[3]{2} )^{log_{ frac{1}{2} }3}= \
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=2*2^{ frac{1}{3}log_{2^{-1}}3 }=2*2^{- frac{1}{3}log_{2}3 }= \
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=2*2^{log_{2}3^{- frac{1}{3} }}=2*3^{- frac{1}{3} }= frac{2}{ sqrt[3]{3} } ( sqrt[3]{2} )^{3+log_{ frac{1}{2} }3}=( sqrt[3]{2} )^3*( sqrt[3]{2} )^{log_{ frac{1}{2} }3}= \
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=2*2^{ frac{1}{3}log_{2^{-1}}3 }=2*2^{- frac{1}{3}log_{2}3 }= \
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=2*2^{log_{2}3^{- frac{1}{3} }}=2*3^{- frac{1}{3} }= frac{2}{ sqrt[3]{3} }](https://tex.z-dn.net/?f=%28+sqrt%5B3%5D%7B2%7D+%29%5E%7B3%2Blog_%7B+frac%7B1%7D%7B2%7D+%7D3%7D%3D%28+sqrt%5B3%5D%7B2%7D+%29%5E3%2A%28+sqrt%5B3%5D%7B2%7D+%29%5E%7Blog_%7B+frac%7B1%7D%7B2%7D+%7D3%7D%3D+%5C+%0A+%5C+%0A%3D2%2A2%5E%7B+frac%7B1%7D%7B3%7Dlog_%7B2%5E%7B-1%7D%7D3+%7D%3D2%2A2%5E%7B-+frac%7B1%7D%7B3%7Dlog_%7B2%7D3+%7D%3D+%5C+%0A+%5C+%0A%3D2%2A2%5E%7Blog_%7B2%7D3%5E%7B-+frac%7B1%7D%7B3%7D+%7D%7D%3D2%2A3%5E%7B-+frac%7B1%7D%7B3%7D+%7D%3D+frac%7B2%7D%7B+sqrt%5B3%5D%7B3%7D+%7D+)
6.
![1) log_{ sqrt{5} }4=log_{5^{ frac{1}{2} }}4=2log_{5}2^2=2*2log_{5}2=4log_{5}2 \
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2) log_{ frac{1}{25} } sqrt[3]{2}=log_{5^{-2}}2^{ frac{1}{3} }=- frac{1}{2}* frac{1}{3}log_{5}2=- frac{1}{6}log_{5}2 \
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3) frac{log_{ sqrt{5} }4}{log_{ frac{1}{25} } sqrt[3]{2} }= frac{4log_{5}2}{- frac{1}{6}log_{5}2 }=4*(-6)=-24
1) log_{ sqrt{5} }4=log_{5^{ frac{1}{2} }}4=2log_{5}2^2=2*2log_{5}2=4log_{5}2 \
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2) log_{ frac{1}{25} } sqrt[3]{2}=log_{5^{-2}}2^{ frac{1}{3} }=- frac{1}{2}* frac{1}{3}log_{5}2=- frac{1}{6}log_{5}2 \
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3) frac{log_{ sqrt{5} }4}{log_{ frac{1}{25} } sqrt[3]{2} }= frac{4log_{5}2}{- frac{1}{6}log_{5}2 }=4*(-6)=-24](https://tex.z-dn.net/?f=++%0A1%29+log_%7B+sqrt%7B5%7D+%7D4%3Dlog_%7B5%5E%7B+frac%7B1%7D%7B2%7D+%7D%7D4%3D2log_%7B5%7D2%5E2%3D2%2A2log_%7B5%7D2%3D4log_%7B5%7D2+%5C+%0A+%5C+%0A2%29+log_%7B+frac%7B1%7D%7B25%7D+%7D+sqrt%5B3%5D%7B2%7D%3Dlog_%7B5%5E%7B-2%7D%7D2%5E%7B+frac%7B1%7D%7B3%7D+%7D%3D-+frac%7B1%7D%7B2%7D%2A+frac%7B1%7D%7B3%7Dlog_%7B5%7D2%3D-+frac%7B1%7D%7B6%7Dlog_%7B5%7D2++++++%5C+%0A+%5C+%0A3%29+frac%7Blog_%7B+sqrt%7B5%7D+%7D4%7D%7Blog_%7B+frac%7B1%7D%7B25%7D+%7D+sqrt%5B3%5D%7B2%7D+%7D%3D++++frac%7B4log_%7B5%7D2%7D%7B-+frac%7B1%7D%7B6%7Dlog_%7B5%7D2+%7D%3D4%2A%28-6%29%3D-24+)
6.
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