SOLUTION: Solve the equation: log x + log (x + 48) = 2 I know the answer is 2 from the answers in the back of the book. I need to know how the solution was solved.

Question 80455This 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 in the back of the book.
I need to know how the solution was solved.
This question is from textbook algebra for college students

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Solve the equation: log x + log (x + 48) = 2
:
Adding logs is the same as multiplying, so you can write it:
log(x*(x+48)) = 2
:
Which is:
log (x^2 + 48x) = 2
:
Find the anti-log of both sides, (anti-log of 2 is 100)
x^2 + 48x = 100
:
Arrange as a quadratic equation
x^2 + 48x - 100 = 0
:
factors to:
(x+50)(x-2) = 0
:
x = -50 and x = +2
:
You can't find the log of negative number, so only x=2 is a solution
:
:
Check solution on a good calc: log(2) + log(50) = 2
:
did this help?
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