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Logarithmic Inequalities

Logarithmic Inequalities - Similar Base


Solve the logarithmic inequality log25(3x2+4x+1)log5(x+1)+1.\log_{25}\left(3 x^2+4x+1\right)\le \log_{5}(x+1)+1.

Solve log2(x13)<log4(x10)+1.\log_2(x-13)<\log_4(x-10)+1.

How many integers xx satisfy the logarithmic inequality log2(x1)log8(2x313x2+20x9)?\log_{2}(x-1)\ge \log_{8}(2x^3-13x^2+20x-9)?

How many integer solutions does the following inequality have: log3(x1)log9(313x2)?\log_{3}(x-1)\le \log_{9}(313-x^2)?

What is the minimum integer xx that satisfies the inequality log2(x4)>log4(x2)?\log_{2}(x-4)>\log_{4}(x-2)?


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