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Logarithmic Inequalities

Logarithmic Inequalities - Different Base


Given log2=0.3010\log 2=0.3010 and log3=0.4771,\log 3=0.4771, solve the inequality log9(x+7)>log8(x+7).\log_9(x+7)>\log_8(x+7).

Solve the inequality log5(log4x)<3.\log_{5}\left( \log_{4}x\right) <3 .

Solve the inequality (log54+log7xlog57)log4511.\left( \log_{5}4+\log_{7}x\cdot \log_{5}7\right)\log_{4}5\le 11.

Solve the inequality log23log332log52xlog54+log58>15.\frac{\log_2 3 \cdot \log_3 32 \cdot \log_5 2^x}{\log_5 4+\log_5 8}> 15.

Solve the inequality log141x>log151x.\log_{14} \frac{1}{x} > \log_{15} \frac{1}{x}.


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