Логарифм, помогите [tex]3^{log _{ \sqrt[3]{9} }4 } + 2^{ ^{ \frac{1}{log _{16} 4} } [/tex]. Created by wotrutest. algebra-ru

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Логарифм, помогите
[tex]3^{log _{ \sqrt[3]{9} }4 } + 2^{ ^{ \frac{1}{log _{16} 4} } [/tex]

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$3^{log_ \sqrt[3]{9}}4}+2^{ \frac{1}{log_{16}4}}=3^{log_(3^{2/3})4} +2^{log_416}=\\\\=3^{ \frac{3}{2}log_34}+2^{log_{2^2}}16=3^{log_34^{3/2}}+2^{ \frac{1}{2}log_216}=\\\\=4^{3/2}+2^{log_2 \sqrt{16}}= (2^2)^{3/2}+ \sqrt{16}=2^3+4=8+4=12$

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