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.
the base is 2.
Animated explanation of logarithms
There are standard notation of logarithms if the base is 10 or e.
logeb is denoted by log b or ln b
List of logarithmic identities
loga1 = 0
logaa = 1
alogab = b
$\log_a(b \cdot c) = \log_ab + \log_ac$
$\log_a\frac{b}{c} = \log_ab - \log_ac$
$\log_ab^n = n \cdot \log_ab$
$\log_{a^n}b = \frac{1}{n}\log_ab, \ \ n\ne0$
Changing the base
$\log_ba=\frac{1}{\log_ab}$
$\log_bc = \frac{\log_ac}{\log_ab}$
loga(b ± c) - there is 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
log2 =
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.