PEAZIT Aha card
Go straight to resources ↓Exponential equations: use the same base
For a positive base other than 1, each power value has exactly one exponent. With equal bases, compare exponents.
| Expression | Meaning |
|---|---|
| 2^(x + 1) = 32 = 2^5 | Both sides have base 2. |
| x + 1 = 5 | Equal values require equal exponents. |
| x = 4 | Subtract 1; the check gives 2^5 = 32. |
One worked example
- 2^(x + 1) = 32 = 2^5Both sides have base 2.
- x + 1 = 5Equal values require equal exponents.
- x = 4Subtract 1; the check gives 2^5 = 32.
Watch out: This method needs a common base a > 0, a ≠ 1. An equation such as 2^x = 7 needs another step, such as a logarithm.
Goal, prerequisites and card origin
What you will learn: Solve an exponential equation by using a common base.
What you need first: Powers and linear equations.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
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For a positive base other than 1, each power value has exactly one exponent. With equal bases, compare exponents.