1. The logarithm and its properties. The logarithm loga x is defined as the power to which the base a must be raised to equal x. 2. Several key properties of logarithms are defined, including: the logarithm in one base can be written in terms of another base; the logarithm of a number to the power of its exponent is that exponent times the logarithm of the number; and logarithms follow laws related to multiplication, division, and powers that parallel those operations with exponents.

1. El logaritmo y sus propiedades
Sea 0 < a, a = 1 y 0 < x
y = loga x sii, por definici´n,
o x = ay
Sean 0 < a, 0 < b, a = 1, b = 1, 0 < x, 0 < y, m = 0, n = 0, 0 < mn, r = 0
loga x
1. logb x = loga b
1
2. logb a = loga b
logb x loga x
3. logb y
= loga y
4. loga (xy) = loga x + loga y
5. loga ( x ) = loga x − loga y
y
6. loga xc = c loga x
c
7. logad xc = d
loga x
8. loga (mn) = loga |m| + loga |n|
9. loga ( m ) = loga |m| − loga |n|
n
10. loga m2c = 2c loga |m|
c
11. logr2d m2c = d
log|r| |m|