Solving Log Inequalities
Read this topicProblems 8
- What is the minimum value of xxx that satisfies the inequality logx≥log3+12logx\log x \ge \log 3 + \frac12 \log xlogx≥log3+21logx?
- Which values of xxx satisfy the following inequality? 2(log3(x))+5<132 (\log_3(x)) + 5 < 132(log3(x))+5<13
- ∣log2(x4−3)+1∣≤1| \log_2(\frac{x}{4}-3) + 1 | \le 1∣log2(4x−3)+1∣≤1 The values of xxx which satisfy this equation are an interval [a,b][a, b][a,b]. What is b−ab-ab−a?
- Solve for xxx. ∣ln(x)∣<3\lvert\ln(x)\rvert<3∣ln(x)∣<3
- A triangle has side lengths log2\log 2log2, log4\log 4log4, and logx\log xlogx, where xxx is an integer. How many possible values of xxx are there?
- Find all real numbers xxx such that ln(x5+1)≥ln(x5−1)\ln(x^5 + 1) \geq \ln(x^5 - 1)ln(x5+1)≥ln(x5−1).
- Solve the inequality log4(x2−20)≥2\log_4(x^2 - 20) \geq 2log4(x2−20)≥2.
- Solve the inequality ln(2x+7)≥ln(23)\ln(2^x + 7) \geq \ln(23)ln(2x+7)≥ln(23).