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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.

What is the range of \(x\) that satisfies the inequality \( 4^x < 16^{6}?\)

What is the range of \(x\) that satisfies the inequality \( \frac{3^{x^2}}{9^{2x}}<1?\)

What is the range of \(x\) that satisfies the inequality \( 4^x < 2^{x+6}?\)

What is the range of \(x\) that satisfies the inequality \( 4^{x-4} > \frac{64^x}{4^{8}}?\)

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