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The
logarithm
of any positive number
N
to the base
b
is
x,
if
x
is the
power to which base
b
must be raised in order to get N. Thus,
N
= bx
or
x = log b
N.
Logarithms to the base 10 are called
common
logarithms,
normally written as the 'log' or 'log 10' of a number. Logarithms to
the base
e =
2.718281828459045...
are called natural logarithms, and are often written 'log e' or 'ln'
of a number. It is more convenient to use natural logarithms
in computations dealing with differentiation. Note that e is
an irrational number. Although not introduced by Napier, the
natural logarithm is sometimes known as the Napierian logarithm.
Log 10 Identities
log10(N)
= log(N) =
x if N=10x
log(10) =
1; log(100) = 2; log(1000) = 3; log(10,000) = 4; log(100,000) = 5...
log(1) = 0
log(0) =
undefined
log(xy) =
log(x) + log(y)
log (x/y) = log(x) - log(y)
log (xy) = y
log(x)
Natural
Logarithmic Identities
loge(N)
= ln(N)
where e = 2.7182818284590452353602874713527...
ln(N) = x if N=ex
ln(e) = 1
ln(xy) =
ln(x) + ln(y)
ln (x/y) = ln(x) - ln(y)
ln (xy) = y
ln(x)
ln(1) = 0
ln(0) =
undefined
General Base
Logarithms
loga(N)
= ln(N)
/ ln(a)
loga(N)
=
logb(N)
/
logb(a)
loga(b)
=
1 /
logb(a)
See Also:
Math Used
in ECE
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