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Logarithms for practical physics

Edexcel IAL Physics · WPH16 Practical Skills in Physics II

Log graphs are the signature skill of Unit 6. First you need to be fluent with the logarithms themselves.

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Two kinds of log

log means log base 10: log 1000 = 3, because 10³ = 1000. The inverse (antilog) is 10^x.
ln means log base e (e = 2.718...): ln e^x = x. The inverse is e^x.

Use ln for exponential relationships involving e (capacitor discharge, absorption, decay, damping); either base works for power laws, but use the same base for both axes.

Rules you need

log(ab) = log a + log b
log(a/b) = log a - log b
log(aⁿ) = n log a
ln(e^-kx) = -kx

These turn y = kxⁿ into log y = n log x + log k, and y = y_0 e^-kx into ln y = -kx + ln y_0.

Logs and units

You can only take the log of a number, so divide by the unit first: log (L / W), ln (V / V). Axis labels are written this way, with brackets. A log has no unit, so neither does the gradient of a log-log graph.

Decimal places

Give log values to a consistent number of decimal places, usually 3 (sometimes 2 is accepted). Round rather than truncate: log 250 = 2.39794 becomes 2.398, not 2.397.

Worked example

Find log 250, ln 0.0450 and the antilog of 1.62.

log 250 = 2.39794, so 2.398
ln 0.0450 = -3.10109, so -3.101
10¹.62 = 41.687, so 41.7

Answer: 2.398, -3.101 and 41.7

Key idea: log is base 10 (inverse 10^x); ln is base e (inverse e^x). log(ab) = log a + log b; log aⁿ = n log a. Take logs of (quantity / unit). Give logs to a consistent 3 d.p., rounded.

Check yourself

Find log 3.0 x 10⁸, to 3 d.p.
Show answer
8.477. log 3.0 x 10⁸ = 8 + log 3.0 = 8.477.
Find ln 0.0450, to 3 d.p.
Show answer
-3.101. ln 0.0450 = -3.101.
log y = 1.62. Find y, to 3 s.f.
Show answer
41.7. y = 10¹.62 = 41.7.
ln y = -0.85. Find y, to 3 s.f.
Show answer
0.427. y = e^-0.85 = 0.427.
Find ln 2, to 3 d.p. (It appears in every half-life and half-thickness calculation.)
Show answer
0.693. ln 2 = 0.693.
Which is equal to log(x³ y)?
- 3 log x + log y
- log 3x + log y
- 3 log x log y
- log x + 3 log y
Show answer
3 log x + log y. log(x³ y) = log x³ + log y = 3 log x + log y.
Which axis label is in the form examiners expect for a log graph?
- log L / W
- L / log W
- log (L / W)
- log L (W)
Show answer
log (L / W). Take the log of the quantity divided by its unit, with brackets.
log 2.6 = 0.41497. Which value should go in a table of log values to 3 d.p.?
- 0.414
- 0.41
- 0.4150
- 0.415
Show answer
0.415. Round, do not truncate, and keep 3 d.p. throughout.

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Last updated 8 November 2026. Spotted a mistake? Tell us.