ln(x+1)+ln(x)=2ln(2)+ln(3)

Solution for ln(x+1)+ln(x)=2ln(2)+ln(3) equation:

Simplifying
ln(x + 1) + ln(x) = 2ln(2) + ln(3)

Reorder the terms:
ln(1 + x) + ln(x) = 2ln(2) + ln(3)
(1 * ln + x * ln) + ln(x) = 2ln(2) + ln(3)
(1ln + lnx) + ln(x) = 2ln(2) + ln(3)

Multiply ln * x
1ln + lnx + lnx = 2ln(2) + ln(3)

Combine like terms: lnx + lnx = 2lnx
1ln + 2lnx = 2ln(2) + ln(3)

Reorder the terms for easier multiplication:
1ln + 2lnx = 2 * 2ln + ln(3)

Multiply 2 * 2
1ln + 2lnx = 4ln + ln(3)

Reorder the terms for easier multiplication:
1ln + 2lnx = 4ln + 3ln

Combine like terms: 4ln + 3ln = 7ln
1ln + 2lnx = 7ln

Solving
1ln + 2lnx = 7ln

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
1ln + -7ln + 2lnx = 7ln + -7ln

Combine like terms: 1ln + -7ln = -6ln
-6ln + 2lnx = 7ln + -7ln

Combine like terms: 7ln + -7ln = 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.