Exponential and logarithmic functions・Form 4 maths・Non-foundation topic

Solve a log equation

A standard method from Exponential and logarithmic functions: the steps and worked examples.

Steps

Use the rules to make a single log on each side.
Remove the log: logₐ(stuff) = c becomes stuff = aᶜ.
Check each answer: the inside of every log must be positive in the original equation.

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 ≈ 1.73

Example 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.