# How do you solve #log_2 (3x-9) - 2 = log_2 (x-4)#?

##### 1 Answer

Jul 30, 2015

Get in the form log(A)=B then re-write in exponential form.

#### Explanation:

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.

x=7.

**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.