Question

rút gọn các biểu thức

a) \(a^{\log_a4}\)

b) \(\log_{a^3}b.\log_ba^2\)

c) \(\log_{a^2}b^3.\log_{b^6}a^4\)

d) \(\dfrac{1}{2}\log_a9-\log_a3\)

e) \(\log_ab^2+\log_{a^2}b^4\)

Answer 1

\(a^{log_a4}=4\)

\(log_{a^3}b.log_ba^2=\dfrac{1}{3}log_ab.2log_ba=\dfrac{\dfrac{2}{3}.log_ab}{log_ab}=\dfrac{2}{3}\)

\(log_{a^2}b^3.log_{b^5}a^4=\dfrac{3}{2}.log_ab.\dfrac{4}{5}log_ba=\dfrac{6}{5}.log_ab.log_ba=\dfrac{6}{5}\)

\(\dfrac{1}{2}log_a9-log_a3=\dfrac{1}{2}log_a3^2-log_a3=log_a3-log_a3=0\)

\(log_ab^2+log_{a^2}b^4=2log_ab+2log_ab=4log_ab\)

Answer 2

a) \(a^{log_a4}=4\)

b) \(log_{a^3}b.log_ba^2=\dfrac{1}{3}log_ab.2log_ba=\dfrac{2}{3}\)

c) \(log_{a^2}b^3.log_{b^6}a^4=log_{a^2}b^3.log_{b^3}a^2=1\)

d) \(\dfrac{1}{2}log_a9-log_a3=log_a\left(9^{\dfrac{1}{2}}\right)-log_a3=log_a3-log_a3=0\)

e) \(log_ab^2+log_{a^2}b^4=2log_a\left|b\right|+2log_a\left|b\right|=4log_a\left|b\right|\)