How To Cancel A Natural Log
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.
Cite This Article
MLA
Crystal, Mike. "How To Cancel A Natural Log" sciencing.com, https://www.sciencing.com/cancel-natural-log-8205306/. 24 April 2017.
APA
Crystal, Mike. (2017, April 24). How To Cancel A Natural Log. sciencing.com. Retrieved from https://www.sciencing.com/cancel-natural-log-8205306/
Chicago
Crystal, Mike. How To Cancel A Natural Log last modified March 24, 2022. https://www.sciencing.com/cancel-natural-log-8205306/