Oblicz: a) log(8) 0,125 b) log(10) 1/1000 c) log(pierwiastek z 2) 16 d) log(pierwiastek z 7) 49 e) log(1/3) 81 f) log(125) 25 g) log(81) 27 Daje naj i z góry dzięki ;)

[latex]log_ab^c=ccdot log_ab\\log_aa=1\===========================\a) log_80,125=log_8frac{1}{8}=log_88^{-1}=-1cdot log_88=-1\\b) logfrac{1}{1000}=log1000^{-1}=log10^{-3}=-3\\c) log_{sqrt2}16=log_{sqrt2}2^4=4log_{sqrt2}2=4log_{sqrt2}left(sqrt2 ight)^2=2cdot4=8\\d) log_{sqrt7}49=log_{sqrt7}7^2=2log_{sqrt7}7=2log_{sqrt7}left(sqrt7 ight)^2=2cdot2=4[/latex] [latex]e) log_frac{1}{3}81=log_frac{1}{3}3^4=4log_frac{1}{3}3=4log_frac{1}{3}left(frac{1}{3} ight)^{-1}=-4\=================================\log_ab=frac{log_cb}{log_ca}\---------------------------\f) log_{125}25=frac{log_525}{log_5125}=frac{log_55^2}{log_55^3}=frac{2}{3}\\g) log_{81}27=frac{log_327}{log_381}=frac{log_33^3}{log_33^4}=frac{3}{4}[/latex]