Scientific Calculator · Practical guide
How to Do Log on a Calculator
Two keys cover every logarithm: log for base 10 and ln for base e — log(1000) returns 3, and the change-of-base trick handles the rest.
At a glance
The Short Answer
Press the log key, type the number, close the parenthesis, and press =. On the calculator above, log(1000) returns 3.000000 because 10³ = 1000. A logarithm answers one question: what exponent turns the base into this number?
Interactive tool
Scientific Calculator
Enter your own values, then compare the result with the examples below.
History
log vs. ln: The Two Keys
The log key is the common logarithm, base 10 — used in pH, decibels, and the Richter scale. The ln key is the natural logarithm, base e ≈ 2.718 — used in continuous growth and decay. Both live in the third row of the keypad:
| You Type | Displayed | Why |
|---|---|---|
| log(100) | 2.000000 | 10² = 100 |
| log(1000) | 3.000000 | 10³ = 1000 |
| ln(e^2) | 2.000000 | ln undoes the power of e |
| ln(10) | 2.302585 | e^2.302585 ≈ 10 |
Any Other Base: Change of Base
For a base like 2 or 5, divide two logs: log base 2 of 32 equals log(32) ÷ log(2) = 1.505150 ÷ 0.301030 = 5.000000, since 2⁵ = 32. The same works with ln: ln(32)/ln(2) also gives exactly 5.
Log Rules That Save Keystrokes
- Product rule — log(a×b) = log(a) + log(b)
- Power rule — log(a^n) = n × log(a), so log(2^10) = 10 × log(2) = 3.010300
- Inverse pair — log(10^x) = x and ln(e^x) = x
One boundary to remember: logarithms of zero and negative numbers are undefined, because no real power of a positive base reaches them — the calculator returns Error rather than a number.
Frequently Asked Questions
Is log the same as ln?
No. log is base 10 and ln is base e ≈ 2.718. They differ by a constant factor: ln(x) = log(x) × ln(10), about 2.3026 times larger.
Why does log(1000) equal 3?
Because 10 raised to the power 3 equals 1000. The logarithm is the exponent needed to reproduce the number from the base.
Can this calculator do log base 2 directly?
Not with a dedicated key, but the change-of-base formula works: divide log of the number by log of 2, such as log(32)/log(2) = 5.
Why do I get Error for log(-5)?
Logarithms are only defined for positive numbers. No real exponent makes 10^anything negative, so the calculator returns Error.