KU Interactive Mathematics
 Course Info Office Hours Exams LiveMath TI Help KU Math Dept Home
 Help Files
 
Logarithmic Equations
 
Question: How would we solve an equation such as the following?
log(x) + log(x + 3) = 1
 
Yours Truly answers: There are two key steps involved in problems of this type. One is to use a logarithm property so that the two logs are combined into one. The other is to convert log into exponential form so that we have a quadratic equation.
 
Observe the following:
log(x) + log(x + 3) = 1
log[x(x + 3)] = 1
x(x + 3) = 101
x2 + 3x = 10
x2 + 3x –10 = 0
(x + 5)(x – 2) = 0
x = 5   or   x = –2
 
Now, x = –2  makes  log(x)  undefined. So, we reject  x = –2.
For  x = 5, both  log(x)  and  log(x + 3)  are defined. So, we accept  x = 5.

Note: The property  y = loga(x)  ⇔  x = ay  is the definition itself of the logarithmic function. In the above problem,  a = 10.
 
 Help Files
 Course Info Office Hours Exams LiveMath TI Help KU Math Dept Home
 KU Interactive Mathematics

Disclaimer • Updated September 4, 2008
Email: mitsuma@kutztown.edu
Phone: +1 (610) 462-WPJW