33.
\(log_2a=\dfrac{log_ba}{log_b2}=\dfrac{log_2b}{log_ab}=\dfrac{log_2b}{\left(\dfrac{b}{8}\right)}=\dfrac{8log_2b}{b}\)
\(\Rightarrow\dfrac{16}{b}=\dfrac{8log_2b}{b}\Rightarrow log_2b=2\Rightarrow b=4\)
\(\Rightarrow log_2a=\dfrac{16}{4}=4\Rightarrow a=2^4=16\)
\(\Rightarrow a+b=20\)
34.
\(\left\{{}\begin{matrix}log_3a+2log_4b=5\\3log_3a-log_4b=1\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}log_3a=1\\log_4b=2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a=3\\b=16\end{matrix}\right.\)
35.
\(log_{\left(\dfrac{a^2}{b}\right)}\left(ab\right)=log_{\left(\dfrac{a^2}{b}\right)}a+log_{\left(\dfrac{a^2}{b}\right)}b=\dfrac{1}{log_a\dfrac{a^2}{b}}+\dfrac{1}{log_b\dfrac{a^2}{b}}=\dfrac{1}{log_aa^2-log_ab}+\dfrac{1}{log_ba^2-log_bb}\)
\(=\dfrac{1}{2-log_ab}+\dfrac{1}{2log_ba-1}=\dfrac{1}{2-3}+\dfrac{1}{\dfrac{2}{3}-1}=-4\)
36.
Câu này đề sai, dữ liệu giả thiết cho vô lý
\(log_{ab}\left(bc\right)=2\Rightarrow bc=\left(ab\right)^2\Rightarrow c=a^2b>c^2.c=c^3>c\) (vô lý)
37.
\(log_{\sqrt{a}}5=4\Rightarrow2log_a5=4\Rightarrow log_a5=2\Rightarrow log_5a=\dfrac{1}{2}\)
\(log_b125=1\Rightarrow3log_b5=1\Rightarrow log_b5=\dfrac{1}{3}\Rightarrow log_5b=3\)
\(log_{a^2b\sqrt{c}}5=\dfrac{1}{log_5a^2b\sqrt{c}}=\dfrac{1}{2log_5a+log_5b+\dfrac{1}{2}log_5c}\)
\(\Rightarrow\dfrac{1}{2.\dfrac{1}{2}+3+\dfrac{1}{2}log_5c}=\dfrac{1}{5}\Rightarrow log_5c=2\Rightarrow log_c5=\dfrac{1}{2}\)
. Chọn đáp án sai:
