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Logarithmic Inequalities

Logarithmic Inequalities - Different Base

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

-8<x<-7

-6<x<-5

-9<x<-8

-7<x<-6

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by Brilliant Staff

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

1<x<4^{125}

1<x<5^{125}

0<x<4^{125}

0<x<5^{125}

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by Brilliant Staff

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

0<x\le 4^{11}

0<x\le 4^{10}

0<x\le 5^{11}

0<x\le 5^{10}

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by Brilliant Staff

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

x<27

x>15

x<4

x>8

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by Brilliant Staff

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

14<x<15

0<x<1

0<x<15

0<x<14

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by Brilliant Staff

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