The various topics on Algebra will be discussed here.

**Logarithms:**

Logarithms are used to express exponential equations in another way. Let a>0 (≠1) and M>0 be such that

a^{x} = M.

Here the number x is called the logarithm of M with base a and we write it mathematically as follows:

x = log_{a} M

log_{2}8 : Value of log 8 to the base 2 is equal to 3.

log_{2}16 : The value of log 16 base 2 is equal to 4.

log_{4}16 : Value of log 16 to the base 4 is equal to 2.

log_{8}16 : Value of log 16 to the base 8 is equal to 4/3.

log_{√2}16: Value of log 16 base √2 equals 8.

log_{3}27 : The value of log 27 base 3 is equal to 3.

log_{√5}125: Value of log 125 base √5 equals 6.

**Complex Numbers:**

A complex number z can be expressed as z=a+ib where a and b are real numbers and i=√-1 is the imaginary complex number.

Learn how to multiply complex numbers.

**Quadratic Equations:**

A quadratic equation is an equation of degree 2 and it is of the form: ax^{2}+bx+c=0 where a, b, and c are real numbers and a is not equal to 0. The value of x is called the root of the given equation. The root can be computed here:

How to solve quadratic equations

The nature of its roots is determined by the discriminant D=b^{2}-4ac.

**Binomial Theorem:**

For two real numbers a and b and for a natural number n, we get the expansion of (a+b)^{n} by using the binomial theorem:

(a+b)^{n} = a^{n} + nC_{1} a^{n-1}b + nC_{2} a^{n-2}b^{2} + … + b^{n},

where nC_{k} is defined by

nC_{k} = $\dfrac{n!}{k! (n-k)!}$.