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Exponential Inequalities

When will a bacteria colony reach a certain size? When will one investment outperform another? Many real-world models use exponential functions, and you'll need these tools to compare them.

Same Base

         

What is the range of \(x\) that satisfies the inequality \( 2^{2x+4} < 2^{3x+8}?\)

If \(6^{a+b} < 6^{8} \) and \(5^{b-a} = 5^{4},\) what is the range of \(a?\)

If \( \frac{3^X}{3\cdot 3^Y} < 1,\) which of the following is true about \(X\) and \(Y?\)

What is the range of \(x\) that satisfies the inequality \( 3^{x+5} < 3^{7}?\)

What is the range of \(x\) that satisfies the inequality \( 2^x < 8?\)

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