How To Take The Natural Log Of A Fraction With X In The Denominator
One way to find the natural logarithm of a fraction is to first convert the fraction to decimal form, then take the natural log. If the fraction includes a variable, however, this method won't work. When you come across the natural log of a fraction with x in the denominator, turn to the properties of logarithms to simplify the expression. Use the property related to division: log(x/y) = log(x) – log(y).
Step 1
Rewrite the natural log of the fraction as the natural log of the numerator minus the natural log of the denominator. If your problem is ln(5/x), for example, rewrite it as ln(5) – ln(x).
Step 2
Take the natural log of the numerator using a scientific calculator. For example, ln(5) = 1.61.
Step 3
Record the answer using your calculated value. For example, ln(5/x) = 1.61 – ln(x).
TL;DR (Too Long; Didn't Read)
If your natural log is part of an algebraic equation, solve the equation using the value of the natural log. For example, if you have the equation 5 = ln(5/x), plug in 1.61 – ln(x): 5 = 1.61 – ln(x). Rearrange the equation to get ln(x) = -3.39. Raise e to the power of both sides: e^[ln(x)] = e^3.39. Raising e to the power of ln(x) results in x, so x = e^3.39 = 29.7.
Cite This Article
MLA
Wakefield, Petra. "How To Take The Natural Log Of A Fraction With X In The Denominator" sciencing.com, https://www.sciencing.com/natural-log-fraction-denominator-8767993/. 21 July 2011.
APA
Wakefield, Petra. (2011, July 21). How To Take The Natural Log Of A Fraction With X In The Denominator. sciencing.com. Retrieved from https://www.sciencing.com/natural-log-fraction-denominator-8767993/
Chicago
Wakefield, Petra. How To Take The Natural Log Of A Fraction With X In The Denominator last modified March 24, 2022. https://www.sciencing.com/natural-log-fraction-denominator-8767993/