Question 604678
log[2](x-5)+log[2](x-11)=4
log[2]((x-5)*(x-11))=4
{{{(x-5)*(x-11) = 2^4}}}
{{{x^2 - 11x - 5x + 55 = 16}}}
{{{x^2 - 16x + 55 = 16}}}
{{{x^2 - 16x + 55 - 16=0}}}
{{{x^2 - 16x + 39=0}}}
(x - 13)*(x - 3) = 0
x - 13 = 0 or x - 3 = 0
x = 13 or x = 3


if we substitute those x values in the logarithm function, x = 3 will make a negative number within the log function:
log[2](x-5)=log[2](3-5) = log[2](-2)
the number in the log function can't be a negative number, so the solution is:
x = 13