ln(7x+2)=ln(2x-8)

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Solution for ln(7x+2)=ln(2x-8) equation:


Simplifying
ln(7x + 2) = ln(2x + -8)

Reorder the terms:
ln(2 + 7x) = ln(2x + -8)
(2 * ln + 7x * ln) = ln(2x + -8)
(2ln + 7lnx) = ln(2x + -8)

Reorder the terms:
2ln + 7lnx = ln(-8 + 2x)
2ln + 7lnx = (-8 * ln + 2x * ln)
2ln + 7lnx = (-8ln + 2lnx)

Solving
2ln + 7lnx = -8ln + 2lnx

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
2ln + 8ln + 7lnx = -8ln + 8ln + 2lnx

Combine like terms: 2ln + 8ln = 10ln
10ln + 7lnx = -8ln + 8ln + 2lnx

Combine like terms: -8ln + 8ln = 0
10ln + 7lnx = 0 + 2lnx
10ln + 7lnx = 2lnx

Add '-2lnx' to each side of the equation.
10ln + 7lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 7lnx + -2lnx = 5lnx
10ln + 5lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
10ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(2 + x) = 0

Ignore the factor 5.

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