Converting Natural Logarithm to Common Logarithm

The logarithm of a number is the power to which the base must be raised in order to obtain this number; for example, the logarithm of 25 with the base 5 is 2 since 52 equals 25. “Ln” stands for the natural logarithm that has the Euler’s constant, approximately 2.71828, as the base. Natural logarithms have many uses in the sciences as well as pure math. The “common” logarithm has 10 as its base and is denoted as “log.” The following formula allows you to take the natural logarithm by using the base-10 logarithm:

(ln(text{number}) = frac{log(text{number})}{log(2.71828)})

TL;DR (Too Long; Didn’t Read)

To convert a number from a natural to a common log, use the equation, ln(​_x_​) = log(​_x_​) ÷ log(2.71828).

Check the Number’s Value

Before you take the logarithm of a number, check its value. Logarithms are defined only for numbers greater than zero, i.e. positive and nonzero. The result of a logarithm, however, may be any real number – negative, positive or zero.

Calculate the Common Log

Enter the number you want to take the logarithm of on your calculator. Press the button “log” to calculate the common log of the number. For example, to find the common log of 24, enter “24” on your calculator and press the “log” key. The common log of 24 is 3.17805.

Calculate Common Log of e

Enter the constant “e” (2.71828) on your calculator and press the button “log” to calculate log10:

(log_{10}(2.71828 ) = 0.43429)

Convert Natural Log to Common Log

Divide the common log of the number by the common log of e, 0.43429, to find the natural logarithm via the common log. In this example:

(ln(24) = frac{1.3802}{0.43429} = 3.17805)