SOLUTION: Solve the equation: log x + log (x + 48) = 2 I know the answer is 2 from the answers page. I need to know how the solution was solved. Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation: log x + log (x + 48) = 2 I know the answer is 2 from the answers page. I need to know how the solution was solved. Thank you.      Log On


   

Question 80453This question is from textbook Algebra for college students
: Solve the equation: log x + log (x + 48) = 2
I know the answer is 2 from the answers page.
I need to know how the solution was solved.
Thank you. This question is from textbook Algebra for college students

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
logx%2Blog%28%28x%2B48%29%29=2
first step is to get the log terms on both sides of the equation:
logx=2-log%28%28x%2B48%29%29
Now raise 10 to both sides of the equation to get rid of the log terms:
10%5E%28%28logx%29%29=10%5E%282-log%28%28x%2B48%29%29%29
Using the log and exponent properties
x=%2810%5E2%29%2F%28x%2B48%29
Now, solve for x:
x%5E2%2B48x-100=0
Factor this...
%28x-2%29%28x%2B50%29=0
You get:
x=2 and x=-50
However, you must plug these answrs back into the original equation to see if it holds true. You will see that x=-50 is an "extraneous root," but x=2 holds true.
so your answer is:
highlight%28x=2%29