[tex]a)\ log_3\ 81 = x\\\\log_3\ 3^4 = x\\\\4\cdot \log_3\ 3 = x\\\\4\cdot 1 = x\\\\4 = x\\\\x=4\\\\\\S=\{4\}[/tex] [tex]b)\ log_2\ \frac{1}{32} = x\\\\log_2\ \big(\frac{1}{2}\big)^5 = x\\\\log_2\ 2^{-5} = x\\\\-5\cdot \log_2\ 2 = x\\\\-5\cdot 1 = x\\\\-5 = x\\\\x=-5\\S=\{-5\}[/tex]
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[tex]c)\ log_{\sqrt{8}} \ 4=x\\\\\frac{log_2 \ 4}{log_2 \ \sqrt{8} } =x\\\\\frac{log_2 \ 2^2}{log_2 \ \sqrt{2^3} } =x\\\\\frac{log_2 \ 2^2}{log_2 \ 2^{\frac{3}{2}} } =x\\\\\frac{2\cdot log_2 \ 2}{\frac{3}{2}\cdot log_2 \ 2} =x\\\\\frac{2\cdot 1}{\frac{3}{2}\cdot 1} =x\\\\\frac{2}{3/2} =x\\\\2\cdot\frac{2}{3} =x\\\\\frac{4}{3} =x\\\\x=\frac{4}{3}\\\\S=\{\frac{4}{3}\}[/tex] [tex]d)\ log_{25} \ 0,2 =x\\\\log_{25} \ \frac{2}{10} =x\\\\log_{25} \ \frac{1}{5} =x\\\\\frac{log_{5} \ \frac{1}{5} }{log_{5} \ 25} =x\\\\\frac{log_{5} \ 5^{-1} }{log_{5} \ 5^2 } =x\\\\\frac{-1 \cdot log_{5} \ 5 }{2\cdot log_{5} \ 5} =x\\\\\frac{-1 \cdot 1 }{2\cdot 1} =x\\\\\frac{-1 }{2} =x\\\\x =-\frac{1}{2}\\\\\\\\S=\{-\frac{1}{2}\}[/tex]
