Use logarithms to solve exponential equations of the form ab^(ct)=d and evaluate with technology.
Solve an exponential inequality by isolating the exponential factor and using logarithms
Problem
What is the solution to the exponential inequality \(2^x>10\)?
Big Picture
What this problem is really about
Treat the related equation as the boundary, then use monotonicity to determine which side of that boundary satisfies the inequality. Taking logarithms preserves order, but the sign of the logarithm you divide by still matters. Finally, keep a strict boundary open because equality does not satisfy a strict inequality.
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