Logarithm

The base a logarithm of number b is the power to which number a must be raised in order to get number b

a^{l o g_{a} b} = b

(l o g_{2} 8 = 3 \Leftrightarrow 2^{3} = 8)

a = 10, l o g_{10} x = l g x

a = e = 2.718, l o g_{e} x = l n x

Important logarithm identities

l o g_{a} a = 1

l o g_{a} 1 = 0

l o g_{a} a^{n} = n

Logarithmic identities

l o g_{a} (x y) = l o g_{a} x + l o g_{a} y

l o g_{a} (\frac{x}{y}) = l o g_{a} x - l o g_{a} y

l o g_{a} x^{n} = n l o g_{a} x

Changing the base of a logarithm

l o g_{a} x = \frac{l o g_{b} x}{l o g_{b} a}

l o g_{a} b \cdot l o g_{b} a = 1

a^{l o g_{b} c} = c^{l o g_{b} a}

l o g_{a} x = l o g_{a^{n}} x^{n}

Keywords: logarithm

Polynomials
Special Binomials
Progressions
Arithmetic progression
Geometric progression
Logarithm
Logarithm
Changing the base of a logarithm
Exponents
Powers
Roots
Roots
Proportionality
Direct and Inversely Proportion
Inequalities
Inequalities
Equations
Quadratic equation
Cubic Equations
Irrational and transcendental equations
Complex numbers
Complex Numbers
Adding and Subtracting Complex Numbers
Multiplying and Dividing Complex Numbers
Power of complex numbers
Roots of complex numbers
Kamatni račun
Interest calculation,
Matrices
Definition, adding & subtracting of matrices
Multiplying matrices