ln(x+2)=ln(5x+6)

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Solution for ln(x+2)=ln(5x+6) equation:


Simplifying
ln(x + 2) = ln(5x + 6)

Reorder the terms:
ln(2 + x) = ln(5x + 6)
(2 * ln + x * ln) = ln(5x + 6)
(2ln + lnx) = ln(5x + 6)

Reorder the terms:
2ln + lnx = ln(6 + 5x)
2ln + lnx = (6 * ln + 5x * ln)
2ln + lnx = (6ln + 5lnx)

Solving
2ln + lnx = 6ln + 5lnx

Solving for variable 'l'.

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

Add '-6ln' to each side of the equation.
2ln + -6ln + lnx = 6ln + -6ln + 5lnx

Combine like terms: 2ln + -6ln = -4ln
-4ln + lnx = 6ln + -6ln + 5lnx

Combine like terms: 6ln + -6ln = 0
-4ln + lnx = 0 + 5lnx
-4ln + lnx = 5lnx

Add '-5lnx' to each side of the equation.
-4ln + lnx + -5lnx = 5lnx + -5lnx

Combine like terms: lnx + -5lnx = -4lnx
-4ln + -4lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-4ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), '-4ln'.
-4ln(1 + x) = 0

Ignore the factor -4.

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