Log Base 5 of 4

Logarithm Calculator
Log base
x

What is log₅ 4?

Answer

log5 4 ≈
0.8614

log5 is the log base 5.

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

log5 4 is the power you raise 5 to, to get 4: 5y = 4.

5⁰ = 1 < 4 < 5 = 5¹, so 0 < log5 4 < 1

log5 4 = ln 4 / ln 5 ≈ 1.386294 / 1.609438 ≈ 0.8614

Oxy1

Answer point ≈ (4, 0.8614).

The curve y = log5 x passes through (1, 0) and (5, 1) and rises: for x > 1 the log is positive, for 0 < x < 1 negative.

Log of 4 in different bases
BaseNotationValue
eln 4≈ 1.3863
10log 4≈ 0.6021
2log₂ 42
5log₅ 4≈ 0.8614

See Also

Recalculate with different values ↑

Log base 5 of nearby numbers

xlog₅ x
10
3≈ 0.6826
4≈ 0.8614
51
7≈ 1.2091
9≈ 1.3652
10≈ 1.4307

FAQ

What is log₅ 4?

log₅ 4 ≈ 0.8614

How to calculate log₅ 4 on a calculator?

Divide the natural logs: log₅ 4 = ln 4 / ln 5 ≈ 1.386294 / 1.609438 ≈ 0.8614.

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