Algebra
Logarithmic Inequalities
Solve the logarithmic inequality \[\log_{25}\left(3 x^2+4x+1\right)\le \log_{5}(x+1)+1.\]
Solve \[\log_2(x-13)<\log_4(x-10)+1.\]
How many integers \(x\) satisfy the logarithmic inequality \[\log_{2}(x-1)\ge \log_{8}(2x^3-13x^2+20x-9)?\]
How many integer solutions does the following inequality have: \[\log_{3}(x-1)\le \log_{9}(313-x^2)?\]
What is the minimum integer \(x\) that satisfies the inequality \[\log_{2}(x-4)>\log_{4}(x-2)?\]