About this video
How to solve exponential equations where the unknown is in the power, by writing both sides with the same base.
What it covers
- Making the bases the same on both sides
- Rewriting a number with that base (25 = 5²; SHIFT FACT on the calculator)
- Moving a + or − constant away first — nothing extra at the base level
- Equating the exponents and checking the answer
Extra worked examples
✍️ Extra example: solve 2x = 32
- 12x = 25Rewrite 32 with a base of 2: 2 × 2 × 2 × 2 × 2 = 32.
- 2x = 5The bases are the same, so the exponents are equal. Check: 2⁵ = 32 ✓
✍️ Extra example: solve 32x − 1 + 4 = 31
- 132x − 1 = 27First take the + 4 to the other side — no + or − may stay with the base.
- 232x − 1 = 3327 written with a base of 3.
- 32x − 1 = 3 → 2x = 4 → x = 2Equate the exponents, then solve.
- 4Check: 33 + 4 = 27 + 4 = 31 ✓Substitute back into the question.
Exercises to try
Work each one out, then click to reveal the answer.
- 1Solve 3x = 81.
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3x = 34, so x = 4 - 2Solve 5x + 1 = 125.
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5x + 1 = 53 → x + 1 = 3 → x = 2 - 3Solve 23x = 64.
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23x = 26 → 3x = 6 → x = 2 - 4Solve 72x − 3 = 7.
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7 = 71 → 2x − 3 = 1 → x = 2 - 5Solve 2x − 1 − 3 = 13.
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2x − 1 = 16 = 24 → x − 1 = 4 → x = 5
