Ln(10-2m)=ln(10-4m)

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Solution for Ln(10-2m)=ln(10-4m) equation:


Simplifying
Ln(10 + -2m) = ln(10 + -4m)
(10 * nL + -2m * nL) = ln(10 + -4m)

Reorder the terms:
(-2mnL + 10nL) = ln(10 + -4m)
(-2mnL + 10nL) = ln(10 + -4m)
-2mnL + 10nL = (10 * ln + -4m * ln)

Reorder the terms:
-2mnL + 10nL = (-4lmn + 10ln)
-2mnL + 10nL = (-4lmn + 10ln)

Solving
-2mnL + 10nL = -4lmn + 10ln

Solving for variable 'm'.

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

Add '4lmn' to each side of the equation.
-2mnL + 4lmn + 10nL = -4lmn + 4lmn + 10ln

Reorder the terms:
4lmn + -2mnL + 10nL = -4lmn + 4lmn + 10ln

Combine like terms: -4lmn + 4lmn = 0
4lmn + -2mnL + 10nL = 0 + 10ln
4lmn + -2mnL + 10nL = 10ln

Add '-10nL' to each side of the equation.
4lmn + -2mnL + 10nL + -10nL = 10ln + -10nL

Combine like terms: 10nL + -10nL = 0
4lmn + -2mnL + 0 = 10ln + -10nL
4lmn + -2mnL = 10ln + -10nL

Reorder the terms:
4lmn + -10ln + -2mnL + 10nL = 10ln + -10nL + -10ln + 10nL

Reorder the terms:
4lmn + -10ln + -2mnL + 10nL = 10ln + -10ln + -10nL + 10nL

Combine like terms: 10ln + -10ln = 0
4lmn + -10ln + -2mnL + 10nL = 0 + -10nL + 10nL
4lmn + -10ln + -2mnL + 10nL = -10nL + 10nL

Combine like terms: -10nL + 10nL = 0
4lmn + -10ln + -2mnL + 10nL = 0

Factor out the Greatest Common Factor (GCF), '2n'.
2n(2lm + -5l + -1mL + 5L) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing m to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(2lm + -5l + -1mL + 5L)' equal to zero and attempt to solve: Simplifying 2lm + -5l + -1mL + 5L = 0 Reorder the terms: 5L + -5l + 2lm + -1mL = 0 Solving 5L + -5l + 2lm + -1mL = 0 Move all terms containing m to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + -5l + 2lm + -5L + -1mL = 0 + -5L Reorder the terms: 5L + -5L + -5l + 2lm + -1mL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + -5l + 2lm + -1mL = 0 + -5L -5l + 2lm + -1mL = 0 + -5L Remove the zero: -5l + 2lm + -1mL = -5L Add '5l' to each side of the equation. -5l + 2lm + 5l + -1mL = -5L + 5l Reorder the terms: -5l + 5l + 2lm + -1mL = -5L + 5l Combine like terms: -5l + 5l = 0 0 + 2lm + -1mL = -5L + 5l 2lm + -1mL = -5L + 5l 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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