Câu 3:
\(\log_a\left(3a^5\right)=\log_aa^5+\log_a3=5+5=10\)
=>Chọn A
Câu 4:
\(\log_2\left(\dfrac{a}{2}\right)=\log_2a-\log_22=\log_2a-1\)
=>Chọn C
Câu 5:
\(\log_2a-3\cdot\log_2b=2\)
=>\(\log_2a-\log_2b^3=2\)
=>\(\log_2\left(\dfrac{a}{b^3}\right)=2\)
=>\(\dfrac{a}{b^3}=4\)
=>\(a=4b^3\)
=>Chọn A
Câu 6:
\(\log\left(100a\right)=\log100+\log_{10}a=2+log\left(a\right)\)
=>Chọn B
Câu 8:
\(\log_a\left(b^2c^3\right)=\log_ab^2+\log_ac^3\)
\(=2\cdot\log_ab+3\cdot\log_ac\)
\(=2\cdot2+3\cdot3=13\)
=>Chọn A
Câu 9:
\(3\cdot\log_2a+2\cdot\log_2b=\log_2a^3+\log_2b^2\)
\(=\log_2\left(a^3b^2\right)=\log_232=5\)
=>Chọn B
Câu 10:
\(P=\log_{a^2}b+\log_{ab^2}b^5=\dfrac{1}{2}\cdot\log_ab+\dfrac{5}{log_bab^2}\)
\(=\dfrac{1}{2}\cdot log_ab+\dfrac{5}{log_ba+log_bb^2}\)
\(=\dfrac{1}{2}\cdot log_ab+\dfrac{5}{\dfrac{1}{log_ab}+2}=\dfrac{1}{2}\cdot2+\dfrac{5}{\dfrac{1}{2}+2}\)
\(=1+5:\dfrac{5}{2}=1+2=3\)
=>Chọn A
. Chọn đáp án sai:
