Solve the equation ln(x + 5) - ln(3) = ln(x - 3).?

Question

Solve the equation ln(x + 5) - ln(3) = ln(x - 3).
a. 2.5
b. 5
c. 7
d. 4.5

Answer 1

ln(x + 5) - ln(3) = ln(x - 3)

Division/subtraction rule of logs:
ln((x + 5) / 3) = ln(x - 3)

Subtract ln(x-3) from both sides:
ln((x + 5) / 3) - ln(x - 3) = 0

Division/subtraction rule of logs:
ln([(x + 5) / 3] / (x - 3)) = 0

Carry out fraction division:
ln((x + 5) / 3(x - 3)) = 0

Definition of ln:
e^0 = (x + 5) / 3(x - 3)

e^0 = 1:
1 = (x + 5) / 3(x - 3)

Cross multiply:
3(x - 3) = x + 5

Distribute:
3x - 9 = x + 5

Subtract x and add 9 to both sides:
2x = 14

Divide both sides by 2:
x = 7


Check answer:
ln(7 + 5) - ln(3) = ln(7 - 3)
ln(12) - ln(3) = ln(4)
ln(12/3) = ln(4)
ln(4) = ln(4)

Answer 2

ln(x + 5) - ln(3) = ln(x - 3)
ln(x+5) - ln(x-3) = ln(3)
ln[(x+5)/(x-3)] = ln(3)

take the exponentials of both sides or make both sides as exponents of e. It will simplify to

(x+5)/(x-3) = 3
(x+5) = 3(x-3)
x + 5 = 3x - 9
x - 3x = -9 - 5
-2x = -14
x = 7

letter c is the answer...

Answer 3

ln(x+5) - ln(3) = ln(x-3)

ln((x+5)/3) = ln(x-3) [since log a - log b = log(a/b)

take out logs

(x+5)/3 = x-3

x+5 = 3x - 9

2x = 14

x = 7

Answer 4

ln(x+5) - ln(3) = ln(x-3)
ln[ (x+5)/3] = ln(x-3)
(x+5)/3 = x-3
x + 5 = 3x - 9
14 = 2x
x = 7, answer c.

Answer 5

the answer is c. 7

Answer 6

(x+5)/3=(x-3)
x+5=3x-9
-2x=-14
x=7

c