ln(7x+6)=ln(5x+14)

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Solution for ln(7x+6)=ln(5x+14) equation:


Simplifying
ln(7x + 6) = ln(5x + 14)

Reorder the terms:
ln(6 + 7x) = ln(5x + 14)
(6 * ln + 7x * ln) = ln(5x + 14)
(6ln + 7lnx) = ln(5x + 14)

Reorder the terms:
6ln + 7lnx = ln(14 + 5x)
6ln + 7lnx = (14 * ln + 5x * ln)
6ln + 7lnx = (14ln + 5lnx)

Solving
6ln + 7lnx = 14ln + 5lnx

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
6ln + -14ln + 7lnx = 14ln + -14ln + 5lnx

Combine like terms: 6ln + -14ln = -8ln
-8ln + 7lnx = 14ln + -14ln + 5lnx

Combine like terms: 14ln + -14ln = 0
-8ln + 7lnx = 0 + 5lnx
-8ln + 7lnx = 5lnx

Add '-5lnx' to each side of the equation.
-8ln + 7lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 7lnx + -5lnx = 2lnx
-8ln + 2lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-8ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), '2ln'.
2ln(-4 + 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 '(-4 + x)' equal to zero and attempt to solve: Simplifying -4 + x = 0 Solving -4 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + x = 0 + 4 x = 0 + 4 Combine like terms: 0 + 4 = 4 x = 4 Add '-1x' to each side of the equation. x + -1x = 4 + -1x Combine like terms: x + -1x = 0 0 = 4 + -1x Simplifying 0 = 4 + -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.

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