ln(4m+2)=ln(5m-7)

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Solution for ln(4m+2)=ln(5m-7) equation: 


Simplifying
ln(4m + 2) = ln(5m + -7)

Reorder the terms:
ln(2 + 4m) = ln(5m + -7)
(2 * ln + 4m * ln) = ln(5m + -7)

Reorder the terms:
(4lmn + 2ln) = ln(5m + -7)
(4lmn + 2ln) = ln(5m + -7)

Reorder the terms:
4lmn + 2ln = ln(-7 + 5m)
4lmn + 2ln = (-7 * ln + 5m * ln)

Reorder the terms:
4lmn + 2ln = (5lmn + -7ln)
4lmn + 2ln = (5lmn + -7ln)

Solving
4lmn + 2ln = 5lmn + -7ln

Solving for variable 'l'.

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

Add '-5lmn' to each side of the equation.
4lmn + -5lmn + 2ln = 5lmn + -5lmn + -7ln

Combine like terms: 4lmn + -5lmn = -1lmn
-1lmn + 2ln = 5lmn + -5lmn + -7ln

Combine like terms: 5lmn + -5lmn = 0
-1lmn + 2ln = 0 + -7ln
-1lmn + 2ln = -7ln

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

Combine like terms: 2ln + 7ln = 9ln
-1lmn + 9ln = -7ln + 7ln

Combine like terms: -7ln + 7ln = 0
-1lmn + 9ln = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-1m + 9) = 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 '(-1m + 9)' equal to zero and attempt to solve:

Simplifying
-1m + 9 = 0

Reorder the terms:
9 + -1m = 0

Solving
9 + -1m = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1m = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1m = 0 + -9
-1m = 0 + -9

Combine like terms: 0 + -9 = -9
-1m = -9

Add 'm' to each side of the equation.
-1m + m = -9 + m

Combine like terms: -1m + m = 0
0 = -9 + m

Simplifying
0 = -9 + m

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.

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