Exponential Inequalities

Exponential Inequalities - Problem Solving


How many positive integers x<1000x<1000 satisfy the inequality x3x+1>xx+139 x^{3x+1} > x^{x+139} ?

Which of the following satisfies the inequality 3y4x2?3^y \geq 4^x - 2 ?

How many integers xx satisfy the inequality 2555<(25)x2<1258(16625)x?\frac{2 ^5}{5 ^5} < \left( \frac{2}{5} \right)^{x^2} < \frac{125}{8} \cdot \left( \frac{16}{625} \right)^x ?

What is the minimum value of xx that satisfies the inequality 22x1272x12802^{2x} - 127 \cdot 2^x -128 \geq 0?

If y=f(x)y=f(x) is the equation of the line which has a slope of 15-\frac{1}{5} and passes through the point (0,5),(0,5), what is the solution to the inequality 0f(5x)10? 0 \leq f(5^x) \leq 10 ?


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