ln(2u)=ln(t+1)

Solution for ln(2u)=ln(t+1) equation:

Simplifying
ln(2u) = ln(t + 1)

Remove parenthesis around (2u)
ln * 2u = ln(t + 1)

Reorder the terms for easier multiplication:
2ln * u = ln(t + 1)

Multiply ln * u
2lnu = ln(t + 1)

Reorder the terms:
2lnu = ln(1 + t)
2lnu = (1 * ln + t * ln)
2lnu = (1ln + lnt)

Solving
2lnu = 1ln + lnt

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
-1ln + 2lnu = 1ln + -1ln + lnt

Combine like terms: 1ln + -1ln = 0
-1ln + 2lnu = 0 + lnt
-1ln + 2lnu = lnt

Add '-1lnt' to each side of the equation.
-1ln + -1lnt + 2lnu = lnt + -1lnt

Combine like terms: lnt + -1lnt = 0
-1ln + -1lnt + 2lnu = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1 + -1t + 2u) = 0

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 '(-1 + -1t + 2u)' equal to zero and attempt to solve:

Simplifying
-1 + -1t + 2u = 0

Solving
-1 + -1t + 2u = 0

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

Add '1' to each side of the equation.
-1 + -1t + 1 + 2u = 0 + 1

Reorder the terms:
-1 + 1 + -1t + 2u = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1t + 2u = 0 + 1
-1t + 2u = 0 + 1

Combine like terms: 0 + 1 = 1
-1t + 2u = 1

Add 't' to each side of the equation.
-1t + t + 2u = 1 + t

Combine like terms: -1t + t = 0
0 + 2u = 1 + t
2u = 1 + t

Add '-2u' to each side of the equation.
2u + -2u = 1 + t + -2u

Combine like terms: 2u + -2u = 0
0 = 1 + t + -2u

Simplifying
0 = 1 + t + -2u

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.