[latex]log_{3} frac{1}{27} =log_{3}( frac{1}{3})^{3}=log_{3}3^{-3}=-3\2log_{3}27-log_{2}16=2log_{3}3^{3}-log_{2}2^{4}=2*3-4=6-4=2 [/latex] [latex]log100+log_{2}64=log10^{2}+log_{2}2^{6}=2+6=8\log_{4}2+log_{7}49= frac{log_{2}2}{log_{2}4} +log_{7}7^{2}= frac{1}{2}+2= frac{5}{2} [/latex] [latex]log_{4}8+log_{4}2= log_{4}(8*2)=log_{4}16=2\log_{3}36-log_{3}4=log_{3} frac{36}{4}=log_{3}9=2 [/latex] [latex]log_{6}32+log_{6}4=log_{6}(32*4)=log_{6}128=log_{6}2^{7}=7log_{6}2=7 frac{log_{2}2}{log_{2}6}=[/latex][latex]7 frac{1}{log_{2}2+log_{2}3}= frac{7}{1+log_{2}3} [/latex]
[latex]log_3frac{1}{27} = log_3 (27)^{-1} = log_33^{-3} = -3\\2log_327-log_216 =2*log_33^3-log_22^4 = 2*3-4 = 6-4 = 2\\log100+log_264 = log10^2 + log_22^6 = 2 +6 = 8\\log_42 +log_749 = log_44^{frac{1}{2}} + log_77^2 = frac{1}{2} +2 = 2,5\\log_48+log_42 = log_4(8*2) = log_416 = log_44^2 = 2\\log_336-log_34 = log_3(36:4) = log_39 = log_33^2 = 2\\log_632+log_64 = log_6(32*4) = log_6128 = log_62^7= 7*log_62=7*frac{log2}{log6}\= ok 2,708[/latex]
