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 log_{a} 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:

Common logarithm: A logarithm with base 10. For example `log_(10) 5`, `log_(10) 7`, `log 7`, `log_(10) C`

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;

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## Comments (2)

i need help

its useful