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Logarithmic Inequalities

Logarithmic Inequalities - Same Base


Solve the logarithmic inequality log3(x9)+log3(x7)<1.\log_3(x-9)+\log_3(x-7)<1.

How many integer solutions does the following inequality have: log3x9+(log3x)210?\log_{3}x^{9}+\left( \log_{3}x \right)^2 \le 10?

If the solution to the inequality (log5x)2<5log5x4 (\log_{5} x)^2 < 5 - \log_{5} x^{4} is a<x<b a < x < b , what is the value of 1ab \frac{1}{ab} ?

Solve the logarithmic inequality log2(15x17)log2(x+16).\log_2 (15x-17) \ge \log_2 (x+16).

How many positive integers xx satisfy the inequality log0.1(x15)log0.1(301x)>0 \log_{0.1} (x-15) - \log_{0.1} (301-x) > 0 ?


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