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

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.