Natural Log of 1.05

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What is ln 1.05?

Answer

ln 1.05 ≈
0.0488

ln is the natural log, base e ≈ 2.71828.

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

ln 1.05 is the power you raise e ≈ 2.71828 to, to get 1.05: ey = 1.05.

e⁰ = 1 < 1.05 < e¹ ≈ 2.7183, so 0 < ln 1.05 < 1

Oxy1

Answer point ≈ (1.05, 0.0488).

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 1.05 in different bases
BaseNotationValue
eln 1.05≈ 0.0488
10log 1.05≈ 0.0212
2log₂ 1.05≈ 0.0704

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
0.5≈ −0.6931
0.9≈ −0.1054
10
1.05≈ 0.0488
1.5≈ 0.4055
2≈ 0.6931
e1

FAQ

What is ln 1.05?

ln 1.05 ≈ 0.0488

What is the difference between ln 1.05 and log 1.05?

ln 1.05 is the logarithm to base e, log 1.05 is to base 10: ln 1.05 ≈ 0.0488, log 1.05 ≈ 0.0212. One is the other divided by ln 10: log 1.05 = ln 1.05 / ln 10 ≈ 0.0212.

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