How to Get Rid of Logarithms

By Tricia Lobo; Updated April 24, 2017
The History of Logarithms

In Algebra II, you will have to solve many equations containing logarithms. Logarithms are mathematical expressions that can be converted into exponential expressions: if log(base b)(x)=a, then b^a=x. You often will see the natural logarithm, ln x, in math problems; ln x can be written as log(base e)(x), in which e is approximately equal to 2.718. When working with logarithms, you will find the possibility of converting them into exponential expressions to be invaluable. This conversion often is the key to getting rid of the logarithm and solving the equation.

Isolate the expression containing the logarithm, so that it is on one side of the equation only. If your expression is ln(x-3)-2=6, add 2 to both sides of the equation to obtain ln(x-3)=8.

Take the exponential of both sides of the equation, to obtain e^(ln(x-3))=ln 8.

Simplify both sides of the equation. You can simplify the left side of the equation by using the property of natural logarithms that e^(ln x) equals x. Therefore, the left side simplifies to x-3, while the right side simplifies to 2.08.

Solve the equation the way you would traditionally solve algebraic equations. Since the equation now is x-3=2.08, add 3 to both sides of the equation to obtain x=5.08.

About the Author

Tricia Lobo has been writing since 2006. Her biomedical engineering research, "Biocompatible and pH sensitive PLGA encapsulated MnO nanocrystals for molecular and cellular MRI," was accepted in 2010 for publication in the journal "Nanoletters." Lobo earned her Bachelor of Science in biomedical engineering, with distinction, from Yale in 2010.