Free calculator
Log calculator (logarithm)
Compute y = log_b(x) for a positive number x and a base b (presets 10, e, 2, or a custom base). Use the Antilog tab for x = b^y. This is math logarithms for spreadsheets and classwork—not server log files, not symbolic equation solving like some algebra apps.
When to use this calculator
Quick checks for common log, natural log, binary log, or another base—then paste the same idea into Sheets or Excel.
- Convert growth multipliers or half-lives when you already think in powers of 2, 10, or e.
- Match
LOG,LN,LOG10, orLOG(x, base)in a workbook after sanity-checking the argument sign. - Pair with the rule of 72 or compound interest tools when you want ln(2) or growth-factor language in context.
The logarithm y = log_b(x) answers: “To what power do we raise b to get x?” So b^y = x. We use the real-number rules you see in spreadsheets: x and b must be positive, and b cannot be 1.
Definition
log_b(x) is the exponent y such that b^y = x. Examples: log_10(100) = 2 because 10^2 = 100; ln(e) = 1 because e^1 = e.
Change of base
For any valid b, log_b(x) = ln(x) / ln(b). That is how one engine computes every base consistently (and how you can reconcile calculator buttons).
Domain (why errors appear)
x must be > 0 in the reals. b must be > 0 and ≠ 1. Antilog b^y can overflow for huge y—the tool stops instead of inventing a number.
What we do not model
Complex numbers, logarithmic regression fits, symbolic simplification of expressions like log(a)+log(b), and logarithmic equations with multiple logs are out of scope—use a CAS or classroom tool when you need that depth.
For doubling time intuition with continuous compounding, see therule of 72 calculator.
For balance growth with deposits, open thecompound interest calculator.
For CAGR from two values, use theCAGR calculator.
Google Sheets & Excel (logarithms)
Common log is base 10; LN is base e; LOG10 is base 10 in Excel. Google Sheets LOG can take an optional second argument for base. Antilog is POWER(base, y).
=LOG10(A1)Or =LOG(A1,10) in Google Sheets. A1 holds a positive number.
=LN(A1)Same as =LOG(A1,EXP(1)) in Sheets when you want the second-argument style.
=LOG(A1, B1)Excel LOG is base-10 only unless you use LOG(number, base) on builds that support the two-argument form—check your version. Sheets documents LOG(value, base).
=POWER(B1, C1)B1 = base, C1 = exponent. For base e, =EXP(C1).
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Frequently asked questions
What does “log” mean on this calculator?
Here log means a logarithm in math: log_b(x) is the power you put on b to get x. It is not application or server logging.
What is the difference between log, ln, and log10?
ln(x) is log_e(x) (natural logarithm). log10(x) is log_10(x) (common logarithm). Many calculators use log for base 10; always check the base. This page lets you pick 10, e, 2, or a custom base so you can match your textbook or sheet.
What is antilog?
Antilog reverses the logarithm: if y = log_b(x), then x = b^y. The Antilog tab computes b^y for the b and y you enter.
Why is log(0) undefined?
No real power y makes b^y = 0 when b > 0. So log_b(0) is undefined in the real numbers—the tool shows an error instead.
How does change-of-base work?
log_b(x) = ln(x) / ln(b) for x > 0 and valid b. It is the standard way to compute arbitrary-base logs with a single natural-log routine.
How do I match this in Excel or Google Sheets?
Use LOG10 or LOG(number,10) for base 10, LN for base e, LOG(number, base) where supported for other bases, and POWER(base, exponent) or EXP for antilogs. Function names can differ by language pack—use Insert function in your app to confirm.
Why might my result differ slightly from another calculator?
Floating-point binary arithmetic can differ in the last digits from a handheld calculator or a CAS. For spreadsheet parity, copy the same formula family as in the Sheets & Excel section.
Can this simplify log expressions or solve log equations?
No. This page evaluates numeric log_b(x) and b^y only. For symbolic algebra or multi-step log equations, use a dedicated computer algebra system or your course’s recommended tool.
Is this tutoring or financial advice?
No. It is a free educational calculator for transparent math—not personalized teaching, grading, or investment guidance.