ACT Preparation / Unit 12 ACT 1117 short lesson, about 20 seconds
Solving by a Common Base
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The idea
If both sides of an exponential equation can be written as powers of the same base, set the exponents equal: if bᵐ = bⁿ, then m = n.
In practice
4^(x + 1) = 8ˣ: 2^(2x + 2) = 2^(3x), so 2x + 2 = 3x, and x = 2.
Where people slip
Rewrite both sides fully before comparing exponents.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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