Solve for X? (Logarithmic Equation)

log9(x5)+log9(x+3)=1

2 Answers
Apr 17, 2017

x=6 and x=4

Explanation:

Recall that logaAB=logaA+logaB and logaa=1.
Therefore, log9(x5)+log9(x+3)=1 can be written as log9{(x5)(x+3)}=log99.
Cancel out log9 on both sides, we have (x5)(x+3)=9; and solving (x5)(x+3)9=0 for x we have x=6,4

Apr 17, 2017

x=6

Explanation:

Using properties of logarithms we can rewrite the left hand side.

log(a)+log(b)=log(ab)

log9((x5)(x+3))=1

Now rewrite both sides in terms of the base 9

9log9((x5)(x+3))=91

rewriting the left hand side we have

(x5)(x+3)=9

x22x+15=9

x22x24=0

(x6)(x+4)=0

x6=0 OR x+4=0

x=6

If we are restricted to the real numbers, we disregard
x=4