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.

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) (Show Source): You can put this solution on YOUR website!

first step is to get the log terms on both sides of the equation:

Now raise 10 to both sides of the equation to get rid of the log terms:

Using the log and exponent properties

Now, solve for x:

Factor this...

You get:
and
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:

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