Bài tự luận · Bài 4
Dạng 1. Thực hiện các phép tính lôgarit
Bài tự luận Lôgarit · Bài 4
(CTST11) Tính giá trị của các biểu thức sau:
a) $\log_{3}45+\log_{3}\frac{1}{5}$;
b) $\log_{4}48-\log_{4}3$;
c) $\log_{2}\frac{16}{3}+2\log_{2}\sqrt{6}$
d) $\frac{1}{3}\log_{3}\frac{9}{7}+\log_{3}\sqrt[3]{7}$.
a) $\log_{3}45+\log_{3}\frac{1}{5}$;
b) $\log_{4}48-\log_{4}3$;
c) $\log_{2}\frac{16}{3}+2\log_{2}\sqrt{6}$
d) $\frac{1}{3}\log_{3}\frac{9}{7}+\log_{3}\sqrt[3]{7}$.
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Lời giải
a) $\log_{3}45+\log_{3}\frac{1}{5}=\log_{3}\left( 45\cdot \frac{1}{5} \right)=\log_{3}9=\log_{3}3^{2}=2$;
b) $\log_{4}48-\log_{4}3=\log_{4}\frac{48}{3}=\log_{4}16=\log_{4}4^{2}=2$;
c) $\log_{2}\frac{16}{3}+2\log_{2}\sqrt{6}=\log_{2}\frac{16}{3}+\log_{2}6=\log_{2}\left( \frac{16}{3}\cdot 6 \right)=\log_{2}32=\log_{2}2^{5}=5$;
d) $\frac{1}{3}\log_{3}\frac{9}{7}+\log_{3}\sqrt[3]{7}=\frac{1}{3}\left( \log_{3}9-\log_{3}7 \right)+\log_{3}7^{\frac{1}{3}}$
$=\frac{1}{3}\log_{3}3^{2}-\frac{1}{3}\log_{3}7+\frac{1}{3}\log_{3}7=\frac{2}{3}\log_{3}3=\frac{2}{3}.$
b) $\log_{4}48-\log_{4}3=\log_{4}\frac{48}{3}=\log_{4}16=\log_{4}4^{2}=2$;
c) $\log_{2}\frac{16}{3}+2\log_{2}\sqrt{6}=\log_{2}\frac{16}{3}+\log_{2}6=\log_{2}\left( \frac{16}{3}\cdot 6 \right)=\log_{2}32=\log_{2}2^{5}=5$;
d) $\frac{1}{3}\log_{3}\frac{9}{7}+\log_{3}\sqrt[3]{7}=\frac{1}{3}\left( \log_{3}9-\log_{3}7 \right)+\log_{3}7^{\frac{1}{3}}$
$=\frac{1}{3}\log_{3}3^{2}-\frac{1}{3}\log_{3}7+\frac{1}{3}\log_{3}7=\frac{2}{3}\log_{3}3=\frac{2}{3}.$