How to Cancel a Natural Log

Logarithms have a number of basic properties that make evaluating them easier.
••• Marek Uliasz/Hemera/Getty Images

In mathematics, the logarithm of any number is an exponent to which another number, called a base, must be raised to produce that number. For example, since 5 raised to the third power is 125, the logarithm of 125 to the base 5 is 3. The natural logarithm of a number is a specific case in which the base is the irrational number e, equal to about 2.7183.

Terminology and Notation

When using e as a base, you write "ln x," with the e subscript implied. This convention is similar to "log x," where base 10 is implied. This is because e and 10 are by far the most common bases found in everyday science and math applications.

Canceling the Natural Log

Two important properties of logarithms make solving problems involving e simpler. These are: e raised to the power of (ln x) = x, and the ln of (e raised to the power of x) = x. For example, to find z in the expression

12 = e to the power of 5z,

take the natural log of both sides to get

ln 12 = ln e to the power of 5z, or

ln 12 = 5z, which reduces to

z = (ln 12)/5, or 0.497.

Related Articles

How to Get Rid of Cubed Power
How to Evaluate Logarithms With Square Root Bases
Laws of Exponents: Powers & Products
How to Get Rid of Logarithms
How to Divide Exponents With Different Bases
How to Simplify Exponents
How to Enter a Subscript on the TI-83
What Are Reciprocal Identities?
How to Solve Logarithms With Different Bases
How to Find the Inverse of a Given Number
How to Determine an Unknown Exponent
How to Calculate Exponents
How to Add & Multiply Exponents
How to Convert Fractions to Exponential Notation
How to Calculate Antilog
How to Factor Monomials
How to Put Base Log on Graphing Calculator
How to Simplify Monomials
What Happens When You Raise a Number to a Fraction?
How to Factorise a Quadratic Expression