Question

Tính giá trị của các biểu thức:

a) \(log_272-\dfrac{1}{2}\left(log_23+log_227\right)\);

b) \(5^{log_240-log_25}\);

c) \(3^{2+log_92}\).

Answer 1

\(a,log_272-\dfrac{1}{2}\left(log_23+log_227\right)\\ =log_272-\dfrac{1}{2}log_2\left(3\cdot27\right)\\ =log_272-log_2\left(81\right)^{\dfrac{1}{2}}\\ =log_272-log_29\\ =log_2\dfrac{72}{9}\\ =log_28\\ =3\)

\(b,5^{log_240-log_25}\\ =5^{log_2\dfrac{40}{5}}\\ =5^{log_28}\\ =5^3\\ =125\)

\(c,3^{2+log_92}\\ =3^{log_9\left(81\cdot2\right)}\\ =3^{\dfrac{1}{2}log_3162}\\ =\left(162\right)^{\dfrac{1}{2}}\\ =\sqrt{162}\\ =9\sqrt{2}\)