Examples with solutions for Change-of-Base Formula for Logarithms: Inequality

Exercise #1

Is inequality true?

\log_{\frac{1}{4}}9<\frac{\log_57}{\log_5\frac{1}{4}}

Video Solution

Answer

Yes, since:

\log_{\frac{1}{4}}9<\log_{\frac{1}{4}}7

Exercise #2

What is the domain of X so that the following is satisfied:

\frac{\log_{\frac{1}{8}}2x}{\log_{\frac{1}{8}}4}<\log_4(5x-2)

Video Solution

Answer

\frac{2}{3} < x

Exercise #3

Given X>1 find the domain X where it is satisfied:

log3(x2+5x+4)log3x<logx12 \frac{\log_3(x^2+5x+4)}{\log_3x}<\log_x12

Video Solution

Answer

1 < x < -2.5+\frac{\sqrt{57}}{2}