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Advanced Logarithmic Worksheets

Inequalities

Advanced

Logarithmic

1. \ln(\frac{1}{x})\ge\ln(x)

1. \ln(\frac{1}{x})\ge\ln(x)

2. \log_{4}(x)+8\ge10

2. \log_{4}(x)+8\ge10

3. \log_{4}(b)\gt 5

3. \log_{4}(b)\gt 5

4. (-\log_{10}(x))\ge0

4. (-\log_{10}(x))\ge0

5. \log_{11}(x+7)\lt 1

5. \log_{11}(x+7)\lt 1

6. \log_{8}(-6x)\lt 1

6. \log_{8}(-6x)\lt 1

7. 0\gt \ln(x-8)

7. 0\gt \ln(x-8)

8. \ln(4x-1)\lt 2

8. \ln(4x-1)\lt 2

9. \ln(2x-3)+\ln(x-1)\gt 0

9. \ln(2x-3)+\ln(x-1)\gt 0

10. \log_{10}(x-2)+\log_{10}(9-x)\lt 1

10. \log_{10}(x-2)+\log_{10}(9-x)\lt 1

Answers

Inequalities

Advanced

Logarithmic

1. 0<x\le 1

2. x\ge 16

3. b>1024

4. 0<x\le 1

5. -7<x<4

6. -\frac{4}{3}<x<0

7. 8<x<9

8. \frac{1}{4}<x<\frac{e^{2}+1}{4}

9. x>2

10. 2<x<4\lor 7<x<9