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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.

# Exponential Inequalities - 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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