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