W zadaniach stosuję wzory
log_ab=\frac{log_cb}{log_ca}
log_a(b_1*b_2)=log_ab_1+log_ab_2
e)
log_{\sqrt2}(6\sqrt3)=log_{\sqrt2}6+log_{\sqrt2}\sqrt3=log_{\sqrt2}2+log_{\sqrt2}3+\frac{log_2\sqrt3}{log_2\sqrt2}=
2+\frac{log_23}{log_22^{\frac{1}{2}}}+\frac{log_23^{\frac{1}{2}}}{log_22^{\frac{1}{2}}}=2+\frac{a}{\frac{1}{2}log_22}+\frac{\frac{1}{2}log_23}{\frac{1}{2}log_22}=
=2+\frac{a}{\frac{1}{2}}+a=
=2+2a+a=3a+2
f)
log_{\frac{1}{9}}\frac{4}{81}=log_{\frac{1}{9}}(\frac{2}{9})^2=2log_{\frac{1}{9}} (\frac{2}{9})=2(log_{\frac{1}{9}}2+log_{\frac{1}{9}}(\frac{1}{9}))=
zastosuję wzór
log_ab=\frac{log_cb}{log_ca}
=2(\frac{log_22}{log_2{\frac{1}{9}}}+1)=2(\frac{1}{log_2{3^{-1}}}+1)=2(\frac{1}{-log_23}+1)=2(\frac{1}{-a}+1)=-\frac{2}{a}+1