log base 2 (3x - 10 - log base 2 (x - 3) = 2?

Question

What does x equal?

Thats:

Log base 2 (3x - 10) - log base 2 (x - 3) = 2?

Answer 1

ok. when you subtract logs with the same base, it's like taking the log of the quotient of what you have in the perentheses.
(log base 2 (y) - log base 2 (x) = log base 2 (y/x) ) When you add logs it's like taking the log of the product.

So,

log base 2 (3x-10) - log base 2 (x-3) = 2

can be rewritten:

log base 2 ((3x - 10) / (x - 3)) = 2

When you have a log base something = to a number, you can raise the number to the base. For example log base 2 (x) = 4. Then 2 ^ 4 = x.

So, in this case:

2 ^ 2 = (3x -10) / (x - 3)

Now multiply both sides by (x - 3)

4x - 12 = 3x - 10

Subtract 3x from each side:

x - 12 = -10

Add 12 to each side:

x= 2

Answer 2

5

Answer 3

x=2. when you have something like log base x (Y) - log base x (Z), it is equal to log base x(Y/Z).