Logarithms Overview

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

Subjects > Mathematics > Logarithms

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

1%

Skills covered in this topic

Add Comment

* Required information
1000

Comments (2)

Gravatar
Jackson Ngasi(Tanzania)says...

i need help

Gravatar
Jackson Ngasi(Tanzania)says...

its useful