a) \(log_216=4\)

b) \(log_3\dfrac{1}{27}=-3\)

c) \(log1000=3\)

d) \(9^{log_312}=144\)

\(log_65=\dfrac{1}{log_56}=\dfrac{1}{log_52+log_53}=\dfrac{1}{a+b}\)

=>Chọn B

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

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: \(log_49=\dfrac{log9}{log4}=\dfrac{log3^2}{log2^2}=\dfrac{2\cdot log3}{2\cdot log2}=\dfrac{log3}{log2}=\dfrac{b}{a}\)

b: \(log_612=\dfrac{log12}{log6}=\dfrac{log2^2+log3}{log2+log3}=\dfrac{2\cdot log2+log3}{log2+log3}\)

\(=\dfrac{2a+b}{a+b}\)

c: \(log_56=\dfrac{log6}{log5}=\dfrac{log\left(2\cdot3\right)}{log\left(\dfrac{10}{2}\right)}=\dfrac{log2+log3}{log10-log2}\)

\(=\dfrac{a+b}{1-a}\)

\(=log_35^2-log_350+log_36\)

\(=log_3\left(\dfrac{25}{50}\cdot6\right)=log_33=1\)

\(2\log_35-\log_350+\dfrac{1}{2}\log_336=\log_35^2-\log_350+\log_336^{\dfrac{1}{2}}=\log_325-\log_350+\log_36=\log_3\left(\dfrac{25}{50}.6\right)=\log_33=1\)

a, ĐK: \(4x+4>0\Rightarrow x>-1\)

\(log_6\left(4x+4\right)=2\\ \Leftrightarrow4x+4=36\\ \Leftrightarrow4x=32\\ \Leftrightarrow x=8\left(tm\right)\)

Vậy x = 8.

b, ĐK: \(x-2>0\Rightarrow x>2\)

\(log_3x-log_3\left(x-2\right)=1\\ \Leftrightarrow log_3\left(x^2-2x\right)=1\\ \Leftrightarrow x^2-2x-3=0\\ \Leftrightarrow\left(x-3\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=3\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\)

Vậy x = 3.

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) \(3In2=2,0794\)