Solve the logarithm?

Question

The site will help u see the problem better
Please show work so I can understand it myself better.
http://docs.google.com/Doc?id=dg4zw6jf_5c6ttxchm

Answer 1

log4 [ (x + 1) / (x - 3) ] = 1
(x + 1) / (x - 3) = 4^1
x + 1 = 4x - 12
3x = 13
x = 13/3
x = 4 ⅓

Answer 2

You need two rules of calculation to solve a problem like this:
Log a - Log b = Log (a/b)

and
Log x = a => b^a = x
where b is the base of the logarithm (in your example b=4)

In this case:
log(x+1) – log(x-3)= 1 (log with base 4)
=> log ((x+1)/(x-3)) = 1
=> (x+1)/(x-3) = 4^1 = 4
=> x +1 = 4x - 12
=> -3x = -13
=> x = 4.333333

Answer 3

Solve: log4(x+1) – log4(x-3)= 1
From the law of logarithm,
we can write the above equation in the following form:
log4[(x + 1)/(x - 3)] = 1
4^1 = (x + 1)/(x - 3)
4 = (x + 1)/(x - 3)
4(x - 3) = (x + 1)
4x - 12 = x + 1
4x - x = 1 + 12
3x = 13
x = 13/3 ANS

teddy boy

Answer 4

Those are two logs in base 4. I'll show that as log_4:

log_4(x+1) - log_4(x-3) = 1

A rule of logs is log(a) - log(b) = log(a/b).

So use that first:
log_4((x+1)/(x-3)) = 1

Now raise both sides upon the base 4. This will cancel the log_4 operation and you just get what is inside the parentheses:
(x+1) / (x-3) = 4^1

The right side simplifies to 4:
(x+1) / (x-3) = 4

Now multiply both sides by (x-3):
x + 1 = 4(x - 3)

Distribute the 4 through the parentheses:
x + 1 = 4x - 12

Subtract x from both sides:
1 = 3x - 12

Add 12 to both sides:
13 = 3x

Divide both sides by 3:
x = 13/3

or as a mixed fraction:
x = 4 1/3

Answer 5

Step 1. [combine] = log(base 4) ((X+1)/(X-3)) = 1
Step 2. [properties of logarithms] = 4 = (X+1)/(X-3)
Step 3. [solve] = 4X - 12 = X + 1
3X = 13

Answer = X = 13/3

Answer 6

log4[(x+1)/(x-3)] = 1
(x+1)/(x-3) = 4^1
x+1 = 4(x-3)
x+1 = 4x - 12
3x = 13
x = 13/3

Answer 7

log4(x+1) – log4(x-3)= 1
log4 (x+1)/(x-3)
(x+1)/(x-3)=4
solve from there.

Answer 8

Solve: log(base4)(x+1) – log(base4)(x-3)= 1
First off log(baseA)A = 1 whatever your base
log(base4)(x+1) – log(base4)(x-3)= log(base4)4
log(base4[(x+1)/(x-3) ]= log(base4)4
So (x+1)/(x-3) = 4 etc etc

Answer 9

(1/16)^(x-3)=[4^(x+1)](1/8)
(1/2)^(4x-12)=[2^(2x+2)](1/(2^3))
2^(-4x+12)=[2^(2x+2)](2^-3)
2^(-4x+12)=[2^(2x+2+(-3))]
2^(-4x+12)=[2^(2x-1)]
so eliminate the 2

so, -4x+12=2x-1
-6x=-13
x=13/6