Solve exponential equations by isolating the power
Solve an exponential equation A0 * b^t = N for t by isolating the power and recognizing it as a power of b. Unlimited questions, five difficulty levels, and a full worked solution every time — free.
Try one
The number of bacteria in a lab culture starts at 4 and multiplies by 2 every week. After how many weeks (t) will it reach 64?
4 · 2t = 64
Answer: 4
See one solved, step by step
The number of bacteria in a lab culture starts at 6 and multiplies by 3 every week. After how many weeks (t) will it reach 486?
6 · 3t = 486
📘 Worked solution
16 · 3t = 486Set up the equation: start at 6, multiply by 3 once per week, and reach 486 after t weeks.
23t = 486 / 6 = 81Divide both sides by 6 to isolate the power of 3.
3Powers of 3: 31 = 3, 32 = 9, 33 = 27, 34 = 81List powers of 3 until one matches 81 — that tells you what t has to be.
4t = 43^4 = 81, so it takes 4 weeks.
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