SOLUTION: Log(x+6)-log(x-3)=1

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Question 1179636: Log(x+6)-log(x-3)=1
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

You start from this equation

    log(x+6) - log(x-3) = 1


It implies, due to properties of logarithms

     = log(10)


Since logarithms are equal, the numbers under the logarithm functions are equal

     = 10


Hence,

    x + 6 = 10*(x-3)

    x + 6 = 10x - 30

    6 + 30 = 10x - x

      36   = 9x

       x   = 36/9 = 4.     ANSWER


You may check, by substituting x= 4 into the original equation, that my answer is correct.

Solved, answered and explained. And completed.


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On logarithms and their properties,  see these introductory lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator
    - Simplifying expressions with logarithms
    - Solving logarithmic equations
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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