a)
log_39=log_33^2=2
b)
log_7\sqrt7=log_77^{\frac{1}{2}}=\frac{1}{2}
c)
log0,01=log\frac{1}{100}=log(\frac{1}{10})^2=10^{-2}=-2
d)
log_{\frac{1}{2}}8=log_{\frac{1}{2}}2^3=log_{\frac{1}{2}}(\frac{1}{2})^{-3}=-3
e)
log_5\frac{1}{25}=log_5(\frac{1}{5})^2=log_55^{-2}=-2
f)
\frac{log_64+2log_63}{log12-log\frac{6}{5}}=\frac{log_6(4*3^2)}{log(12:\frac{6}{5})}=\frac{log_636}{log(\not12^2*\frac{5}{\not6^1})}=\frac{log_66^2}{log10}=\frac{2}{1}=2
g)
9^{1-log_35}=log_33^{2(1-log_35)}=3^{2-2log_35}=3^{log_39-log_35^2}=3^{log_3\frac{9}{25}}=\frac{9}{25}
a^{log_ax}=x wzór