ВЫЧИСЛИТЬ![latex]log _{8} 5^{2log _{25}32 } [/latex] [latex]log _{3} (7 \sqrt{3})-log_{3} (7)[/latex] [latex] \frac{1}{4}^{log _{ \frac{1}{4} }7-3 } [/latex]

[latex]1)log _{8} 5^{2log _{25}32 }=log _{8} (5^2)^{log _{25}32 }= log _{8} (25^{log _{25}32 })=log_8{32}=log_{2^3}{2^5}= \\ \\ = \frac{5}{3} log_22= \frac{5}{3} [/latex] [latex]2)log _{3} (7 \sqrt{3})-log_{3} (7)=log_3 \frac{7 \sqrt{3} }{7}=log_3 \sqrt{3}= \frac{1}{2} [/latex] [latex] 3)\frac{1}{4}^{log _{ \frac{1}{4} }7-3 } =\frac{1}{4}^{log _{ \frac{1}{4} }7} \cdot \frac{1}{4}^{-3} =7\cdot 4^3=7\cdot 64=448[/latex]