Algebra

# Exponential Inequalities - Base < 1

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

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

If $0 the solution set to $a is $\alpha Find $-2\alpha+3\beta.$

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

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

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