ln(x)+ln(x+2)=ln(3)+ln(5)

Solution for ln(x)+ln(x+2)=ln(3)+ln(5) equation:

Simplifying
ln(x) + ln(x + 2) = ln(3) + ln(5)

Multiply ln * x
lnx + ln(x + 2) = ln(3) + ln(5)

Reorder the terms:
lnx + ln(2 + x) = ln(3) + ln(5)
lnx + (2 * ln + x * ln) = ln(3) + ln(5)
lnx + (2ln + lnx) = ln(3) + ln(5)

Reorder the terms:
2ln + lnx + lnx = ln(3) + ln(5)

Combine like terms: lnx + lnx = 2lnx
2ln + 2lnx = ln(3) + ln(5)

Reorder the terms for easier multiplication:
2ln + 2lnx = 3ln + ln(5)

Reorder the terms for easier multiplication:
2ln + 2lnx = 3ln + 5ln

Combine like terms: 3ln + 5ln = 8ln
2ln + 2lnx = 8ln

Solving
2ln + 2lnx = 8ln

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-8ln' to each side of the equation.
2ln + -8ln + 2lnx = 8ln + -8ln

Combine like terms: 2ln + -8ln = -6ln
-6ln + 2lnx = 8ln + -8ln

Combine like terms: 8ln + -8ln = 0
-6ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-3 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

Move all terms containing l to the left, all other terms to the right.

Simplifying
ln = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

Move all terms containing l to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Add '-1x' to each side of the equation.
x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
0 = 3 + -1x

Simplifying
0 = 3 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.