\(a,A=log_23\cdot log_34\cdot log_45\cdot log_56\cdot log_67\cdot log_78\\ =log_28\\ =log_22^3\\ =3\\ b,B=log_22\cdot log_24...log_22^n\\ =log_22\cdot log_22^2...log_22^n\\ =1\cdot2\cdot...\cdot n\\ =n!\)

\(log_{12}21=\dfrac{log_321}{log_312}=\dfrac{log_3\left(7\cdot3\right)}{log_3\left(2^2\cdot3\right)}=\dfrac{log_37+log_33}{log_34+log_33}\)

\(=\dfrac{log_37+1}{log_32^2+1}=\dfrac{log_37+1}{2\cdot log_32+1}=\dfrac{b+1}{2a+1}\)

a: \(log_{\dfrac{1}{4}}8=log_{2^{-2}}2^3=\dfrac{-3}{2}\cdot log_22=-\dfrac{3}{2}\)

b: \(log_45\cdot log_56\cdot log_68\)

\(=log_45\cdot\dfrac{log_46}{log_45}\cdot\dfrac{log_48}{log_46}\)

\(=log_48=log_{2^2}2^3=\dfrac{3}{2}\)

Đáp án A.

a) \(log_69+log_64=log_636=2\)

b) \(log_52-log_550=log_5\left(2:50\right)=-2\)

c) \(log_3\sqrt{5}-\dfrac{1}{2}log_550=-1,0479\)

a) \(log_29\cdot log_34=4\)

b) \(log_{25}\cdot\dfrac{1}{\sqrt{5}}=-\dfrac{1}{4}\)

c) \(log_23\cdot log_9\sqrt{5}\cdot log_54=\dfrac{1}{2}\)

a) \(log_315=2,4650\)

c) \(3In2=2,0794\) 

a) \(\ln\left(\sqrt{5}+2\right)+\ln\left(\sqrt{5}-2\right)=ln\left(\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\right)=\ln\left(\left(\sqrt{5}\right)^2-2^2\right)=ln\left(5-4\right)=\ln1=\ln e^0=1\)

b) \(\log400-\log4=\log\dfrac{400}{4}=\log100=\log10^{10}=10.\log10=10.1=10\)

c) \(\log_48+\log_412+\log_4\dfrac{32}{2}=\log_4\left(8.12.\dfrac{32}{2}\right)=\log_4\left(1024\right)=\log_44^5=5.\log_44=5.1=5\)

a: \(=ln_2\left[\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)\right]=ln1=0\)

b: \(=log\left(\dfrac{400}{4}\right)=log\left(100\right)=10\)

c: \(=log_4\left(8\cdot12\cdot\dfrac{32}{3}\right)=log_4\left(32\cdot32\right)=5\)