Natural Log of 1000

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What is ln 1,000?

Answer

ln 1,000 ≈
6.9078

ln is the natural log, base e ≈ 2.71828.

≈ — the logarithm is irrational; the value is rounded to 4 decimal places.

ln 1,000 is the power you raise e ≈ 2.71828 to, to get 1,000: ey = 1,000.

e⁶ ≈ 403.4288 < 1,000 < e⁷ ≈ 1,096.6332, so 6 < ln 1,000 < 7

Oxy

Answer point ≈ (1,000, 6.9078), beyond the drawing (the arrow points to it).

The curve y = ln x passes through (1, 0) and (e, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.

Log of 1,000 in different bases
BaseNotationValue
eln 1,000≈ 6.9078
10log 1,0003
2log₂ 1,000≈ 9.9658

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
50≈ 3.9120
60≈ 4.0943
100≈ 4.6052
1,000≈ 6.9078
1,380≈ 7.2298
9,297≈ 9.1374
10,000≈ 9.2103

FAQ

What is ln 1,000?

ln 1,000 ≈ 6.9078

What is the difference between ln 1,000 and log 1,000?

ln 1,000 is the logarithm to base e, log 1,000 is to base 10: ln 1,000 ≈ 6.9078, log 1,000 = 3. One is the other divided by ln 10: log 1,000 = ln 1,000 / ln 10 = 3.

What does log without a base mean?

At school and on a calculator, log x without a base is the common log, base 10: log 100 = 2. In Python, math.log(x) is the natural log ln x; in Excel, LN is the natural log and LOG is base 10.

See Also