### Logarithms Overview

Logarithms were invented independently by John Napier, a Scotsman and by Joost Burgi, a Swiss in early 1620s.

Subjects > Mathematics > Logarithms

Before moving direct into the problems of logarithms, let's see what we need to know about logarithms.

#### Meaning of Logarithms

"Logarithm" comes from two Greek words; "logos" meaning "proportion or ratio" and "arithmos" meaning a "number" which together makes "ratio-number".

Logarithm is the inverse function to exponentation, as it answers the question how many of one number do we multiply to get another number?, that means the logarithm of a given number x is the exponent to which another fixed number, the base x, must be raised to produce that number x.

The logarithms of a positive real number x with respect to base b (a positive real number and b ≠ 1) is the exponent by which b must be raised to give x.
From above definition, it means: b^y = X which implies that y = log_b X
log is denoted loga x pronounced log of x to base a or the base-a, logarithm of x or the logarithm, base a of x.

#### Types of logarithms

There are two types of Logarithms:

1. Common logarithm: A logarithm with base 10. For example log_(10) 5, log_(10) 7, log 7, log_(10) C
2. Natural logarithm: A logarithm with base e, e is a constant whose value is approximately 2.718. For example log_e 4 = ln 4, log_e x = ln x,
ln is used to specify that it is a natural logarithm.

#### Rules of Logarithms

If X > 0, Y > 0, a > 0, b > 0 and a ne 1, b ne 1 and n is any real number, then;

1. log_a a = 1
2. log_a 1 = 0
3. log_a X^n = nlog_a X
4. log_a X + log_a Y = log_a (X*Y)
5. log_a X - log_a Y = log_a (X/Y)
6. log_a X = (log X)/(log a)
7. log_a X = log_b X * log_a b
8. log_a b * log_b a = 1
9. log_a b = 1/(log_b a)
10. a^(log_a X) = X

Now, let's move in. Solved Logarithmic questions

Recommended Lessons

Before moving direct into the problems of logarithms, let's see what we need to know about logarithms.

#### Meaning of Logarithms

"Logarithm" comes from two Greek words; "logos" meaning "proportion or ratio" and "arithmos" meaning a "number" which together makes "ratio-number".

Logarithm is the inverse function to exponentation, as it answers the question how many of one number do we multiply to get another number?, that means the logarithm of a given number x is the exponent to which another fixed number, the base x, must be raised to produce that number x.

The logarithms of a positive real number x with respect to base b (a positive real number and b ≠ 1) is the exponent by which b must be raised to give x.
From above definition, it means: b^y = X which implies that y = log_b X
log is denoted loga x pronounced log of x to base a or the base-a, logarithm of x or the logarithm, base a of x.

#### Types of logarithms

There are two types of Logarithms:

1. Common logarithm: A logarithm with base 10. For example log_(10) 5, log_(10) 7, log 7, log_(10) C
2. Natural logarithm: A logarithm with base e, e is a constant whose value is approximately 2.718. For example log_e 4 = ln 4, log_e x = ln x,
ln is used to specify that it is a natural logarithm.

#### Rules of Logarithms

If X > 0, Y > 0, a > 0, b > 0 and a ne 1, b ne 1 and n is any real number, then;

1. log_a a = 1
2. log_a 1 = 0
3. log_a X^n = nlog_a X
4. log_a X + log_a Y = log_a (X*Y)
5. log_a X - log_a Y = log_a (X/Y)
6. log_a X = (log X)/(log a)
7. log_a X = log_b X * log_a b
8. log_a b * log_b a = 1
9. log_a b = 1/(log_b a)
10. a^(log_a X) = X

Now, let's move in. Solved Logarithmic questions

Recommended Lessons