log(base)5 8 - log(base)5 (6-x) = log(base)5 x
My textbook writes that the answer to this problem is x = 4 or 2. How would I go about getting this answer?

Question

log(base)5 8 - log(base)5 (6-x) = log(base)5 x
My textbook writes that the answer to this problem is x = 4 or 2. How would I go about getting this answer?

freckles · Answer

do you know the quotient rule for log thingys ?

freckles · Answer

$$\log_a(x)-\log_a(y)=\log_a(\frac{x}{y})$$

sighn0more · Answer

Yep! So far i know that it's log5 ( 8/(6-x) )

freckles · Answer

cool so you have:
$$\log_5(\frac{8}{6-x})=\log_5(x) \implies \frac{8}{6-x}=x$$

freckles · Answer

now you could multiply both sides by (6-x)

freckles · Answer

8=x(6-x)

freckles · Answer

you have a quadratic equation to solve
expand

freckles · Answer

and put into ax^2+bx+c=0 
you can try to factor 
or use the quadratic formula or complete the square or whatever

sighn0more · Answer

Ohhh, I see now. I'll work the rest of this out. Thank you!

freckles · Answer

k