Logarithm(log, lg, ln)

If b = ac <=> c = logab
a, b, c
are real numbers and b > 0, a > 0, a ≠ 1
a
is called "base" of the logarithm.
Example: 23 = 8 => log28 = 3
the base is 2.

Logarithm - an animated example

There are standard notation of logarithms if the base is 10 or e.

log10b = lg b
logeb = ln b

Properties of logarithms:

loga1 = 0
logaa = 1
alogab = b

loga(b.c) = logab + logac
loga(b/c) = logab - logac
logabn = n.logab

$log_ba=\frac{1}{log_ab}$

$log_bc = \frac{log_ac}{log_ab}$

$log_{a^n}b = \frac{1}{n}log_ab, \ \ n\ne0$

loga(b ± c) - there are no such a formula.

Antilogarithm

logab = logac ⇔ b = c
logab = c ⇔ ac = b, where b > 0, a > 0 and a ≠ 1

logab > logac ⇔ if a > 1 then b > c,
      if 0 < a < 1 then b < c

Logarithmic calculator

Select a logarithm base:
log2 =

Graphs of logarithmic functions

Graphs of logarithmic functions

It shows that when x = 1, log = 0; when x -> 0 => log -> -∞; when x -> ∞ log -> ∞

If you have any question go to our forum about logarithms.


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