Back to Express exponential solutions as logarithms — Problem 1 · Task Set 59

HSF.LE.A.4 Tutor Intake — Solving Exponential Equations with Logarithms

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Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-le-a-4

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Which is the correct first step to solve $500 \cdot 2^{0.1t} = 4000$ ?

Take $\log$ of both sides: $\log(500 \cdot 2^{0.1t}) = \log(4000)$

Divide both sides by 500: $2^{0.1t} = 8$

Subtract 500 from both sides: $2^{0.1t} = 3500$

Divide both sides by 2: $500 \cdot 0.1t = 2000$