Question

\[\log_{2} (x-2)+\log_{2} (8-x)-\log_{2} (x-5)=3\]

Answer 1

Are you aware of the properties of logs?

Answer 2

Product,Quotient,and Power Law right?

Answer 3

Mhm. The first 2 are a product, right?

Answer 4

Yup then followed by quotient,then I am stuck.

Answer 5

what about the more basic property of logs?\[\log_a(b) = x -> a^x = b\]

Answer 6

Are you suggesting that I solve the left side then use the basic properties of log? to change it's form?

Answer 7

I was suggesting something like that but I'm getting unsolvable/unfactorable quadratics so I'm not sure.

Answer 8

\[\log_2(x−2)+\log_2(8−x)−\log_2(x−5)=3\\\log_2\frac{(x-2)(8-x)}{x-5}=3\\\frac{(x-2)(8-x)}{x-5}=8\]
Then I'm like "what the **** is this ****?!"

Answer 9

comes out to a quadratic

x^2 - 2x +30 = 0

Answer 10

sorry thats x^2 -2x - 24 = 0

Answer 11

just solve for x

Answer 12

Should I write both positive and negative or logarithms are only positive?