Logarithm is the inverse operation to exponentiation.
A logarithm is the inverse operation of exponentiation. It is a mathematical operation used to determine how many times a certain number, known as the base, must be multiplied by itself to reach another number.
The Relation: y = bx ⇆ logb(y) = x
Example: 64 = 26 ⇆ log264 = 6
| Logarithm Operations |
Euler's Constant
The base of the natural logarithm.
¸ = ➜ 2.718281...
Natural Antilogarithm
Calculates the natural antilogarithm of value or expression (e^x).
ȶ 2 = ➜ 7.389056...
Common Antilogarithm
Calculates the common antilogarithm of value or expression (10^x).
ȵ 2 = ➜ 100
| Logarithm Functions |
Log (Logarithm Base 10)
Calculates the common logarithm (log10) of value or expression.
▸ Calculate Log10(1000)
log 1 0 0 0 = ➜ 3
Ln (Natural Logarithm)
Calculates the natural logarithm (base e = loge) of value or expression.
▸ Calculate Ln<(1000)
ln 1 0 0 0 = ➜ 6.907755...
Logarithm Rules:
| Product Rule | logb(x‧y) = logb(x) + logb(y) |
| Quotient Rule | logb(x/y) = logb(x) - logb(y) |
| Product Rule | logb(xy) = y ‧ logb(x) |
| Base Change Rule |
logb(x) = logc(x) / logc(b) log2(8) = log10(8) / log10(2) |
| Natural logarithm | ln(x) = loge(x) |