Verified answer

Hi,

They want you to combine the log terms, which means you're going to have to use properties of logs.

1. The first is that log (x) ^ y = y log (x) and vice versa. So you can move an exponent in front of the log as a multiplier; and you could move a number that multiplies an entire log as an exponent:

so

1. 2 log 2 (x) - log 2 (x-3) = 3 + log 2 (2) First Step: replace 2 log 2(x) = log 2 (x^2)

2. log 2 (x^2) - log 2 (x-3) = 3 + log 2 (2)

The next thing we can do is use the log property that log (x) - log (y) = log (x/y) (when all have the same base); so let's combine the terms on the left hand side

3. log 2 [ x^2 / x-3] = 3 + log 2(2); then; log 2 (2) is asking you; 2 ^ x = 2. 2 to what power gives us 2. in this case we can see that log 2 (2) = 1; since 2 ^ 1 = 2.

log 2 [ x^2 / x-3] = 3 +1

log 2 [x^2 / x-3] = 4

Then write the log in exponent form:

2^ 4 = x^2 / x -3

16 = x^2 / x-3

Now you can just solve like an algebra problem (note that x doesn't equal 3; note also that x must be greater than 3 if you look at the original log equation since we have log 2 (x-3)...)

Multiplying both sides by x-3

16x - 48 = x ^2

x^2 -16 x + 48 = 0

(x-4)(x-12) = 0

x = 4 or x = 12 <----answer

Good luck!

-Devon Review

2 log2(x) − log2(x - 3) = 3 + log2(2)

-(log(x-3)-2 log(x))/(log(2)) = 4

-(log(x-3)-2 log(x))= log(16)

log(16 (x-3)) = 2 log(x)

x = 4 or 12

log2(x*2)-log2(x-3)=log2(8)+log2(2)

log2(x*2/x-3)=log2(16)

x*2/x-3=16

x*2-16x+48=0 .......> x=4 and 12

to answer this u have to know this rules:loga+logb=logab and loga-logb=loga/b

also i replaced 3 with log2(8),hope u get it!