47.
\(log_{18}42=\dfrac{log_242}{log_218}=\dfrac{log_2\left(6.7\right)}{log_2\left(\dfrac{36}{2}\right)}=\dfrac{log_26+log_27}{2log_26-log_22}=\dfrac{a+b}{2a-1}\)
Cả 4 đáp án đều sai
48.
\(a^{log_37}=9\Rightarrow7^{log_3a}=9\)
\(\Rightarrow log_3a=log_79\)
\(\Rightarrow a=3^{log_79}=3^{2.log_73}\)
\(\Rightarrow a^{log_3^27}=3^{2log_73.log_3^27}=3^{2log_37}=3^{log_349}=49\)
Tương tự: \(b=7^{log_{11}7}\Rightarrow b^{log_7^211}=7^{log_{11}7.log_7^211}=7^{log_711}=11\)
\(c=11^{log_{25}11}\Rightarrow c^{log_{11}^225}=11^{log_{25}11.log_{11}^225}=11^{log_{11}25}=25\)
\(\Rightarrow T=49+11+25=85\)
49.
\(\dfrac{a}{b}=\dfrac{log_xy}{log_zy}=\dfrac{log_yz}{log_yx}=log_xz\Rightarrow log_zx=\dfrac{b}{a}\)
\(log_{xyz}\left(y^5z^3\right)=5log_{xyz}y+3log_{xyz}z=\dfrac{5}{log_yxyz}+\dfrac{3}{log_zxyz}\)
\(=\dfrac{5}{1+log_yx+log_yz}+\dfrac{3}{1+log_zx+log_zy}\)
\(=\dfrac{5}{1+\dfrac{1}{a}+\dfrac{1}{b}}+\dfrac{3}{1+\dfrac{b}{a}+b}=\dfrac{5ab}{ab+a+b}+\dfrac{3a}{ab+a+b}=\dfrac{5ab+3a}{ab+a+b}\)
50.
\(log_{\dfrac{\sqrt{a}}{b}}\sqrt[3]{ba}=\dfrac{1}{3}log_{\dfrac{\sqrt[]{a}}{b}}b+\dfrac{1}{3}log_{\dfrac{\sqrt[]{a}}{b}}a\)
\(=\dfrac{1}{3log_b\dfrac{\sqrt[]{a}}{b}}+\dfrac{1}{3log_a\dfrac{\sqrt[]{a}}{b}}=\dfrac{1}{3\left(\dfrac{1}{2}log_ba-1\right)}+\dfrac{1}{3\left(\dfrac{1}{2}-log_ab\right)}\)
\(=\dfrac{1}{3\left(\dfrac{1}{6}-1\right)}+\dfrac{1}{3\left(\dfrac{1}{2}-3\right)}=-\dfrac{8}{15}\)
57.
\(log_{\dfrac{1}{a}}\dfrac{1}{b^5}=log_{a^{-1}}b^{-5}=5log_ab\)
59.
\(log_aa^2b^5=log_aa^2+log_ab^5=2+5log_ab\)
60.
\(log_3a^3+log_3b^2=4\Rightarrow log_3\left(a^3b^2\right)=4\)
\(\Rightarrow a^3b^2=3^4=81\)
. Chọn đáp án sai:
