How to Cancel a Natural Log

The natural log is an important logarithmic scale that is used to model many natural phenomena. The base of this logarithm is a number known as "e." This base is sometimes referred to as "Euler's number," after the mathematician Leonard Euler. This "e" is a special irrational integer that is not to be confused with "Euler's Constant." The cancellation of the natural logarithm is used extensively in calculus, and to a smaller extent in algebra, to simplify expressions, such as equations, integrals, and differentials.

Instructions

    • 1

      Use the standard logarithm rules to simplify any natural logarithm expression. The pertinent rules in this matter are the division, multiplication, and exponent rules of logarithms. This often results in one logarithm being turned into many, for example, Ln(x/2) = Ln(x) - Ln(2).

    • 2

      Evaluate any natural logarithms with non-variable arguments. The Ln(2) from above would evaluate to approximately 0.6931.

    • 3

      Raise each term, including previously evaluated non-variable numbers, the the base "e."This simply means make all values in the expression an exponent of e. For example, from above, Ln(x) - 0.6931 = e^Ln(x) - e^0.6931.

    • 4

      Simplify the expression. Remove both the "e" and "Ln" portion of any term which contains both. Continuing from above: e^Ln(x) - e^0.6931 = x - e^0.6931. This resulting expression can be evaluated using standard algebraic manipulation and a calculator to solve for the value of "x."

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