Question

rút gọn các biểu thức

a) \(log_{a^4}b^4.log_ba^5\)

b) \(log_{a^3}b^2.log_ba^4\)

c) \(log_{a^{15}}b^7.log_{b^{49}}a^{30}\)

d) \(log_{a^{2021}}b^{2020}.log_{b^{4040}}a^{6063}\)

 

Answer 1

\(log_{a^4}b^4.log_ba^5=\dfrac{1}{4}.4.log_ab.5.log_ba=5.log_ab.log_ba=5\)

\(log_{a^3}b^2.log_ba^4=\dfrac{1}{3}.2.log_ab.4.log_ba=\dfrac{8}{3}.log_ab.log_ba=\dfrac{8}{3}\)

\(log_{a^{15}}b^7.log_{b^{49}}a^{30}=\dfrac{1}{15}.7.log_ab.\dfrac{1}{49}.30.log_ba=\dfrac{2}{7}log_ab.log_ba=\dfrac{2}{7}\)

\(log_{a^{2021}}b^{2020}.log_{b^{4040}}a^{6063}=\dfrac{1}{2021}.2020.log_ab.\dfrac{1}{4040}.6063.log_ba=\dfrac{3}{2}\)