Solve aˣ = N (x in the index)
A standard method from Exponential and logarithmic functions: the steps and worked examples.
Steps
- Take log of both sides: x log a = log N.
- x = log N ÷ log a.
- Use the calculator and round only at the end, usually to 3 significant figures.
Worked examples
Example 1: Solve 3^(x+1) = 20, correct to 3 significant figures.
(x + 1) log 3 = log 20
x + 1 = log 20 / log 3 ≈ 2.7268
x ≈ 1.73Example 2: Solve log₂(x + 1) = 3.
x + 1 = 2³ = 8
x = 7 check: log₂8 = 3 ✓For the whole topic, read Exponential and logarithmic functions: key points, common mistakes and how the DSE tests it.