Log of 0.9 (Base 10)

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What is log 0.9?

Answer

log 0.9 ≈
−0.0458

log here is the common log, base 10.

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

log 0.9 is the power you raise 10 to, to get 0.9: 10y = 0.9.

10⁻¹ = 1/10 < 0.9 < 1 = 10⁰, so −1 < log 0.9 < 0

log 0.9 = ln 0.9 / ln 10 ≈ −0.105361 / 2.302585 ≈ −0.0458

Oxy

Answer point ≈ (0.9, −0.0458).

The curve y = log x passes through (1, 0) and (10, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.

Log of 0.9 in different bases
BaseNotationValue
eln 0.9≈ −0.1054
10log 0.9≈ −0.0458
2log₂ 0.9≈ −0.1520

See Also

Common log of nearby numbers

FAQ

What is log 0.9?

log 0.9 ≈ −0.0458

What is the difference between log 0.9 and ln 0.9?

ln 0.9 is the logarithm to base e, log 0.9 is to base 10: ln 0.9 ≈ −0.1054, log 0.9 ≈ −0.0458. One is the other divided by ln 10: log 0.9 = ln 0.9 / ln 10 ≈ −0.0458.

What is e?

e ≈ 2.71828 is the base of the natural logarithm: ln x is the logarithm of x to base e, so ln e = 1. It is an irrational number, like π.