Exponential Inequalities

Exponential Inequalities - Base < 1


What is the solution set to 132(12)2x+14?\frac{1}{32}\leq\left(\frac{1}{2}\right)^{2x+1} \leq 4?

What is the solution set to 0.5x+416?0.5^{x+4}\geq16?

If 0<a<b,0<a<b, the solution set to a<axb1x<ba<a^xb^{1-x}<b is α<x<β.\alpha<x<\beta. Find 2α+3β.-2\alpha+3\beta.

What is the smallest integer xx that satisfies (12)x<16?\left(\frac{1}{2}\right)^x<16?

If the solution to 127<(19)x<2187\frac{1}{27}<\left(\frac{1}{9}\right)^x<2187 is α<x<β,\alpha<x<\beta, what is α+β?\alpha+\beta?


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