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
ax = M.
Here the number x is called the logarithm of M with base a and we write it mathematically as follows:
x = loga M
log28 : Value of log 8 to the base 2 is equal to 3.
log216 : The value of log 16 base 2 is equal to 4.
log416 : Value of log 16 to the base 4 is equal to 2.
log816 : Value of log 16 to the base 8 is equal to 4/3.
log√216: Value of log 16 base √2 equals 8.
log327 : The value of log 27 base 3 is equal to 3.
log√5125: 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: ax2+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=b2-4ac.
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 = an + nC1 an-1b + nC2 an-2b2 + … + bn,
where nCk is defined by
nCk = $\dfrac{n!}{k! (n-k)!}$.
Matrix:
Determinant:
Reciprocal of 0 | 1/0 is equal to