SOLUTION: log(x) + log(x − 48) = 2

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Question 1111531: log(x) + log(x − 48) = 2
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.
log(x) + log(x - 48) = 2  ====>


x*(x-48) = 100


x^2 - 48x - 100 = 0


(x-50)*(x+2) = 0  ====>


The last equation has the roots  x= 50  and  x= -2.


But since  x  and  (x-48)  must be positive under the logarithm,  only one root survives:  x= 50.


Answer.  x = 50.

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On logarithms and their properties,  see the lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Solving logarithmic equations
    - Using logarithms to solve real world problems
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.



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