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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 - Different Base

Solve the inequality $$2^{5x}\ge 5^{22-5x}.$$

If the solution to the inequality $$2 ^{1-5x} \le 50 ^{5x}$$ is $$x\ge k,$$ what is $$10^{10k}?$$

Solve for $$x:$$ $3^{-3x+12}\leq11.$

Given that $$\log2=0.301,$$ what is the largest integer $$x$$ that satisfies $2^{x-3}<10^{2}?$

Solve for $$x:$$ $16^{x+2}\geq27^{-2x+3}.$

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