Solving 3²ˣ⁻¹ = 7ˣ⁺²

Algebra 2 · Axiom Academy

EXAMPLE Solving 3^ 2x-1 = 7^ x+2 Using logarithms to solve an exponential equation whose two sides share no common base Solve 3^ 2x-1 = 7^ x+2 for x . Excellent work! You've solved an exponential equation with two bases that can't be matched. Remember: Spot when logs are needed: the bases can't be rewritten with a common base — like 3 and 7 Apply the same logarithm to both sides: this keeps the equation balanced Use the Power Rule: brings each exponent down as a coefficient Solve algebraically: expand, collect the x terms, factor, then divide to isolate x Leave it exact or approximate: This technique — take logs, apply the Power Rule, then solve algebraically — works for any exponential equation whose bases can't be matched. Practice spotting it whenever the variable is stuck in an exponent with no common base in sight.

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