Natural Log of 1.5

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What is ln 1.5?

Answer

ln 1.5 ≈
0.4055

ln is the natural log, base e ≈ 2.71828.

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

ln 1.5 is the power you raise e ≈ 2.71828 to, to get 1.5: ey = 1.5.

e⁰ = 1 < 1.5 < e¹ ≈ 2.7183, so 0 < ln 1.5 < 1

Oxy1

Answer point ≈ (1.5, 0.4055).

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 1.5 in different bases
BaseNotationValue
eln 1.5≈ 0.4055
10log 1.5≈ 0.1761
2log₂ 1.5≈ 0.5850

See Also

Recalculate with different values ↑

Natural log of nearby numbers

xln x
0.9≈ −0.1054
10
1.05≈ 0.0488
1.5≈ 0.4055
2≈ 0.6931
e1
3≈ 1.0986

FAQ

What is ln 1.5?

ln 1.5 ≈ 0.4055

What is the difference between ln 1.5 and log 1.5?

ln 1.5 is the logarithm to base e, log 1.5 is to base 10: ln 1.5 ≈ 0.4055, log 1.5 ≈ 0.1761. One is the other divided by ln 10: log 1.5 = ln 1.5 / ln 10 ≈ 0.1761.

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