How do you solve log_3x+log_3(x-8)=2?

1 Answer
Mar 31, 2018

Thus, x=9 is the valid solution

Explanation:

log_3 x+log_3 (x-8)=2

logm+logn=logmn

log_3 x+log_3 (x-8)=log_3 x(x-8)

log_3 x(x-8)=2

x(x-8)=3^2

x(x-8)=9

x^2-8x=9

x^2-8x-9=0

x^2-9x+1x-9=0

x(x-9)+1(x-9)=0

(x+1)(x-9)=0

x=-1, x=9

x=-1,9

Here, x needs to be a positive number .

Thus, x=9 is the valid solution