Câu 30:
\(a^{log_{\sqrt{a}}5}=a^{log_{a^{\dfrac{1}{2}}}5}\)
\(=a^{2\cdot log_a5}=a^{log_a5^2}=25\)
=>Chọn A
Câu 29:
\(C=log_2\left(a^2b\right)=log_2a^2+log_2b\)
\(=2\cdot log_2a+log_2b\)
\(=2\cdot3+5=11\)
=>Chọn B
Câu 27:
\(log_{\dfrac{1}{a^2}}\left(a\sqrt{a}\right)=log_{a^{-2}}\left(a^{\dfrac{3}{2}}\right)\)
\(=\dfrac{1}{-2}\cdot\dfrac{3}{2}=\dfrac{-3}{4}\)
=>Chọn B
Câu 26:
\(3\cdot loga+2\cdot logb=1\)
=>\(log\left(a^3\right)+log\left(b^2\right)=1\)
=>\(log\left(a^3b^2\right)=1\)
=>\(a^3b^2=10\)
=>Chọn C
Câu 25:
\(P=log_{\sqrt{2}}a-log_2b-1\)
\(=log_{2^{\dfrac{1}{2}}}a-log_2b-1\)
\(=2\cdot log_2a-log_2b-1\)
\(=log_2a^2-log_2b-1\)
\(=log_2\left(\dfrac{a^2}{b}\right)-1\)
\(=log_2\left(\dfrac{8b}{b}\right)-1=log_28-1=3-1=2\)
=>Chọn A
Câu 23:
\(\log a^3b^2=\log a^3+\log b^2=3\cdot\log a+2\cdot\log b\)
=>Chọn C
Câu 22:
\(P=2^{log_2a}+log_a\left(a^b\right)=a+b\)
=>Chọn D
Câu 21:
4<13
0<0,5<1
=>\(log_{0,5}4>log_{0,5}13\)
=>\(1>3^{log_{0,5}4}>3^{log_{0,5}13}\)
=>1>a>b
=>Chọn B
. Chọn đáp án sai:
