ln(3m-7)=ln(2m+9)

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Solution for ln(3m-7)=ln(2m+9) equation: 


Simplifying
ln(3m + -7) = ln(2m + 9)

Reorder the terms:
ln(-7 + 3m) = ln(2m + 9)
(-7 * ln + 3m * ln) = ln(2m + 9)

Reorder the terms:
(3lmn + -7ln) = ln(2m + 9)
(3lmn + -7ln) = ln(2m + 9)

Reorder the terms:
3lmn + -7ln = ln(9 + 2m)
3lmn + -7ln = (9 * ln + 2m * ln)

Reorder the terms:
3lmn + -7ln = (2lmn + 9ln)
3lmn + -7ln = (2lmn + 9ln)

Solving
3lmn + -7ln = 2lmn + 9ln

Solving for variable 'l'.

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

Add '-2lmn' to each side of the equation.
3lmn + -2lmn + -7ln = 2lmn + -2lmn + 9ln

Combine like terms: 3lmn + -2lmn = 1lmn
1lmn + -7ln = 2lmn + -2lmn + 9ln

Combine like terms: 2lmn + -2lmn = 0
1lmn + -7ln = 0 + 9ln
1lmn + -7ln = 9ln

Add '-9ln' to each side of the equation.
1lmn + -7ln + -9ln = 9ln + -9ln

Combine like terms: -7ln + -9ln = -16ln
1lmn + -16ln = 9ln + -9ln

Combine like terms: 9ln + -9ln = 0
1lmn + -16ln = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(m + -16) = 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 '(m + -16)' equal to zero and attempt to solve:

Simplifying
m + -16 = 0

Reorder the terms:
-16 + m = 0

Solving
-16 + m = 0

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

Add '16' to each side of the equation.
-16 + 16 + m = 0 + 16

Combine like terms: -16 + 16 = 0
0 + m = 0 + 16
m = 0 + 16

Combine like terms: 0 + 16 = 16
m = 16

Add '-1m' to each side of the equation.
m + -1m = 16 + -1m

Combine like terms: m + -1m = 0
0 = 16 + -1m

Simplifying
0 = 16 + -1m

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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