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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.

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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