How do you solve log_3(x+4)-log_3x=2log3(x+4)log3x=2?

1 Answer
Dec 14, 2015

x = 1/2x=12

Explanation:

The relevant law of logarithms that will help us here is the following:

log_z A - log_z B = log_z (A/B)logzAlogzB=logz(AB)

where AA and BB can be any expression and zz is the base.

Applying this law to our equation will give us

log_3 ((x+4)/x) = 2log3(x+4x)=2

From here we can simply raise 33 to both sides of the equation.

3^(log_3 ((x+4)/x)) = 3^23log3(x+4x)=32

On the left-hand side, the 33 will cancel with the log_3log3 leaving us with

(x+4)/x = 9x+4x=9

Solving for xx yields x = 1/2x=12.