Question

Tính :

a) \(4^{\log_23}\)

b) \(27^{\log_92}\)

c) \(9^{\log_{\sqrt{3}}2}\)

d) \(4^{\log_827}\)

 

 

Answer 1

a) \(4^{log^3_2}=\left(2^2\right)^{log^3_2}=\left(2^{log^3_2}\right)^2=3^2=9\).
b) \(27^{log^2_9}=\left(3^3\right)^{log^2_{3^2}}=3^{3.\dfrac{1}{2}.log^2_3}=\left(3^{log^2_3}\right)^{\dfrac{3}{2}}=2^{\dfrac{3}{2}}=\sqrt{8}\).
c) \(9^{log^2_{\sqrt{3}}}=9^{log^2_{9^{\dfrac{1}{4}}}}=9^{4.log^2_9}=\left(9^{log^2_9}\right)^4=2^4=16\).
d) \(4^{log^{27}_8}=2^{2.log^{27}_{2^3}}=2^{\dfrac{2}{3}.log^{27}_2}=\left(2^{log^{3^3}_2}\right)^{\dfrac{2}{3}}=\left(3^3\right)^{\dfrac{2}{3}}=3^2=9\).