Question

look at the attachement and solve the asked questions fast please

Answer 1

2
$log_5\ 7^{-3\ log_7\ 5}=-3\ log_7\ 5*log_5\ 7=-3$
3.
$5^x=7,\ \ 5^y=3\\\\3^{log_5\ 7}-7^{log_5\ 3}\\\\=3^x-7^y\\\\=(5^y)^x-(5^x)^y=0$
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4.
$a^2=b^3=c^5=d^6\\a=d^3,\ \ b=d^2,\ \ c=d^{\frac{6}{5}}\\abc=d^{\frac{31}{5}}\\\\log_d\ abc=\frac{31}{5}$
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1
$log_{\frac{1}{5}}\ 27=-3\ log_5\ 3\\\\log_{125}\ 81=\frac{4}{3}Log_5\ 3\\\\25^{(\frac{1}{2}-3log_5\ 3+\frac{4}{3}log_5\ 3)}=(5^2)^{\frac{1}{2}-\frac{5}{3}Log_5\ 3}\\\\.\ \ \ =\frac{5}{5^{\frac{10}{3}Log_5\ 3}}\\\\=.\ \ \ \frac{5}{(5^{Log_5\ 3})^{\frac{10}{3}}}\\\\=.\ \ \ \frac{5}{(3)^{\frac{10}{3}}}\\\\=5*3^{-3.333...}$