How do you solve #log_2 (3x-9) - 2 = log_2 (x-4)#?
Get in the form log(A)=B then re-write in exponential form.
Get all logs on one side, then use quotient rule for logarithms
We know that
Multiply both sides by x-4, subtract 3x and add 16 to both sides.
IMPORTANT: When solving log equations, check for extraneous solutions: Log of 0 or less is undefined for real numbers so make sure that substituting your value for x will not give you a 0 or negative inside the log function. In this case:
so our solution is ok.