HELP!! LOgs!!!! ALgebra 2?

Question

Can anyone help me out on this one i just keep getting it wrong and i have no idea how. :)

log(base2) (X+4) - log (base2) (x-3) =3

Answer 1

Well, ok, we have:

log_2(x + 4) - log_2(x - 3) = 3

First, we'll use one of the properties of logs:

loga - logb = loga/b

So, we have:

log_2{(x + 4)/(x - 3)} = 3

Now, what that expression above says is: "The power you put on 2 to get (x + 4)/(x - 3) is 3." So, we rewrite it as such:

2^3 = (x + 4)/(x - 3)

8(x - 3) = x + 4

8x - 24 = x + 4

7x - 24 = 4

7x = 28

x = 4

There you go.

Answer 2

To do those, keep in mind the operation conversion that occurs once you adjust c= base^potential to a logarithm. The log version is log(base)c=potential So permit's attempt #6. this is the log version of (x+4)^3 = one hundred twenty five. So what selection cubed is one hundred twenty five. situations UP, the respond is 5. So x+4=5 and x=a million.

Answer 3

Okay. I'm assuming you know basic log properties.
When you've got log subtraction with the same base, it turns into division. So, you'd end up with:
log(base 2) (x+4/x-3)=3
Now, by changing the equation into normal exponent form, you should get:
2^3=x+4/x-3
8=x+4/x-3
8x-24=x+4
7x=28
x=4

Answer 4

log(base2) (X+4) - log (base2) (x-3) =3

log(base2)[(x + 4)/(x - 3)] = 3
2^3 = (x + 4)/(x - 3)
8(x - 3) = (x + 4)
8x - 24 = x + 4
8x - x = 24 + 4
7x = 28
x = 4 ANS

Hope I help you.

teddy boy

Answer 5

Let log be log to base two in the following:-
log (x + 4) - log (x - 3) = 3
log [ (x + 4) / (x - 3) ] = 3
(x + 4) / (x - 3) = 2 ³
(x + 4) / (x - 3) = 8
x + 4 = 8x - 24
28 = 7x
x = 4

Answer 6

formulae:
1) log(basex)y = z => y = x^z
2) logx - logy = log(x/y)

log(base2)(x+4) - Log(base2)(x-3) = 3
=>log(base2) [(x+4)/(x-3)] = 3
=>(x+4)/(x-3) = 2^3 = 8
=>x+4 = 8x - 24
=> x = 4
(Ans)

Answer 7

okay, combine the left hand side to make one log

log(base 2) [(x+4)/(x-3)] = 3

now, set the right hand side, 3, as a log of base 2

log(base 2) [(x+4)/(x-3)] = log(2^3)

and now you can cancel the logs on both sides, leaving you with a nice, clean, solvable equation.

x+4/x+3 = 2^ 3

you can do the rest :P

Answer 8

2^log(base2)(x+4) - 2^log(base2)(x-3)=2^3
(x+4)-(x-3)=8
7=8
No solution!

Answer 9

log(x) - log(y) = log(x/y)

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

(x+4)/(x-3) = 2^3 = 8

28 = 7x

4 = x

Answer 10

log2(x+4)/(x-3)=3
8=(x+4)/(x-3)
8x-24=x+4
7x=28
x=4