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?

Answer 1

do you know the quotient rule for log thingys ?

Answer 2

\[\log_a(x)-\log_a(y)=\log_a(\frac{x}{y})\]

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

8=x(6-x)

Answer 7

you have a quadratic equation to solve
expand

Answer 8

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

Answer 9

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

Answer 10

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