# What is x if #log_4 x=2 - log_4 (x+6)#?

##### 2 Answers

See process below

#### Explanation:

In this type of equations, our goal is to arrive to an expresion like

Lets see

We know that

So, we have

by quadratic formula

Solutions are

#### Explanation:

#"using the "color(blue)"laws of logarithms"#

#•color(white)(x)logx+logy=log(xy)#

#•color(white)(x)log_b x=nhArrx=b^n#

#" add "log_4(x+6)" to both sides"#

#log_4x+log_4(x+6)=2#

#log_4x(x+6)=2#

#x(x+6)=4^2=16#

#x^2+6x-16=0#

#(x+8)(x-2)=0#

#x=-8" or "x=2#

#x>0" and "x+6>0#

#"thus "x=-8" is invalid"#

#rArrx=2" is the solution"#