Skip main navigation

Hurry, only 4 days left to get one year of Unlimited learning for £249.99 £174.99. New subscribers only. T&Cs apply

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

It's your turn on Inequalities with logarithms and exponentials

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]

This article is from the free online

Created by

## Reach your personal and professional goals

Unlock access to hundreds of expert online courses and degrees from top universities and educators to gain accredited qualifications and professional CV-building certificates.

Join over 18 million learners to launch, switch or build upon your career, all at your own pace, across a wide range of topic areas.

Start Learning now