Solve the logarithmic equation algebraically

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Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If there is no solution, enter NO SOLUTION.)

log4 x + log4(x − 6) = 2
x =
May 3rd, 2015

log4(x)+log4(x-6)=2
log4((x)(x-6))=2
(x)(x-6)=4^2
(x)(x-6)=16
x^2-6x-16=0
(x-8)(x+2) = 0
.
x = {-2, 8}
  Since log cannot have negatives,
x = 8

Please let me know if you have any other questions and best me if you are satisfactory.   


May 3rd, 2015

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