Logarithm Log Calculator

The Logarithm is the inverse function of exponents. Addition, multiplication, subtraction and division are the key mathematical operations that are used in Log equations.

In Exponents, when a number b, the base, is raised to a certain power y, the exponent, then you can get the value x

x = b^y;

The logarithm of base b is the inverse operation, that provides the output y (the above exponent) from the input x.

Logarithm of a positive real number x with respect to base b is the exponent by which b must be raised to get x

 then y = log_bx; where b is the base

It is pronounced as the logarithm of x to base b

Logarithm Base

The logarithm base 10 (b = 10) is called the decimal or common logarithm and is commonly used in science and engineering.

The natural logarithm has the number e (that is b ≈ 2.718) as its base; it is commonly used in mathematics and physics.

Common Log Formulas and Rules

Logarithm Product Rule

• log_b(xy) = log_bx + log_by

Logarithm Quotient Rule

• log_b(x/y) = log_bx – log_by

Logarithm Power Rule

• log_b(x^z) =z log_bx
• log_b(x)^1/p = (log_bx)/p

How to Change log base in logarithms?

Logarithm change of base rule and formula to change log base from b to k

log_b(x) = log_k(x) / log_k(b)

Logarithm base switch rule

log_b(c) = log_c(c) / log_c(b)

as  log_c(c) = 1, therefore

log_b(c) = 1/ log_c(b)