It’s your turn on inequalities with logarithms and exponentials, 1

Do your best in trying to solve the following problems. In any case some of them are solved in the video and all of them are solved in the pdf file below.

Exercise 1.

Can you tell which of the following inequalities are true, without using a calculator?

a) (log_23<log_32)

b) (log_23<dfrac{3}{2})

c) (log_32<dfrac{2}{3})

Exercise 2.

Solve the following inequality [Big(frac{1}{3}Big)^{-frac{7}{x}}-Big(frac{1}{3}Big)^{x+8}>0.]

Exercise 3.

Discuss the solutions of the following inequality, as (b>0), (bneq 1) varies in (mathbb{R}): [log_{b}(2x-1)>log_bx.]

Exercise 4.

Solve the inequality [log_2x-frac{2}{log_2x}+1>0] [This exercise is solved just in the pdf below]