On a TI-84 Plus CE
- Decide the base b and the value x you want log_b(x) for.
- Press MATH → logBASE( and enter logBASE(x, b). (Older OS: use log(x)/log(b).)
Tip: Change of base always works on any calculator: log_b(x) = ln(x) / ln(b) = log(x) / log(b).
Evaluate a logarithm to any base
Work out log to any base directly - useful for solving exponential equations and for logarithmic scales.
In short: A logarithm to any base asks what power the base must be raised to in order to give a number. Most calculators have only log (base 10) and ln (base e), so for other bases you use the change-of-base rule: log base b of x equals log x divided by log b. Some models also have a dedicated log-base function.
When you'd use this
- The log isn't base 10 or base e, so the LOG/LN buttons alone don't directly give it.
- Solving an exponential equation, e.g. 5ˣ = 200, which rearranges to a logarithm.
- Working with a logarithmic scale (e.g. pH, decibels, Richter) that uses a specific base.
- Checking a change-of-base calculation done by hand.
At a glance: TI-84 Plus CE, Casio fx-CG50 and TI-Nspire CX compared
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | Press MATH → logBASE( and enter logBASE(x, b). (Older OS: use log(x)/log(b).) | Use the log_□□ template (math templates) or type log(b, x) via OPTN → CALC. | Type log(x, b) directly - the base goes after the comma. |
On a Casio fx-CG50 and fx-CG100
- Decide the base b and the value x you want log_b(x) for.
- Use the log_□□ template (math templates) or type log(b, x) via OPTN → CALC.
Tip: Change of base always works on any calculator: log_b(x) = ln(x) / ln(b) = log(x) / log(b).
On a TI-Nspire CX
- Decide the base b and the value x you want log_b(x) for.
- Type log(x, b) directly - the base goes after the comma.
Tip: Change of base always works on any calculator: log_b(x) = ln(x) / ln(b) = log(x) / log(b).
Related guides
Try it yourself
Here's a real IB-style question that uses exactly this technique.
Easy
Calculator
Paper 2
[2 marks]
Evaluate log₅(200), to 3 significant figures.
3.29
Mark it
Correct
2 / 2 marks
Worked solution & mark scheme:
M1 Change of base: log(200) ÷ log(5)
A1 3.29
Common questions
When would I need to evaluate a logarithm to any base in IB Maths?
Work out log to any base directly - useful for solving exponential equations and for logarithmic scales. The log isn't base 10 or base e, so the LOG/LN buttons alone don't directly give it. Solving an exponential equation, e.g. 5ˣ = 200, which rearranges to a logarithm.
How do I evaluate a logarithm to any base on a TI-84 Plus CE?
1. Decide the base b and the value x you want log_b(x) for. 2. Press MATH → logBASE( and enter logBASE(x, b). (Older OS: use log(x)/log(b).)
How do I evaluate a logarithm to any base on a Casio fx-CG50 and fx-CG100?
1. Decide the base b and the value x you want log_b(x) for. 2. Use the log_□□ template (math templates) or type log(b, x) via OPTN → CALC.
How do I evaluate a logarithm to any base on a TI-Nspire CX?
1. Decide the base b and the value x you want log_b(x) for. 2. Type log(x, b) directly - the base goes after the comma.
What should I watch out for when I evaluate a logarithm to any base?
Change of base always works on any calculator: log_b(x) = ln(x) / ln(b) = log(x) / log(b).
How are marks awarded when I evaluate a logarithm to any base in an IB exam?
In the worked example on this page (2 marks, Paper 2), the marks are: M1: Change of base: log(200) ÷ log(5); A1: 3.29.
Practise with your calculator
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.