Algebra
# Exponential Inequalities

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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