ln(5)=ln(6+x)

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


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

Reorder the terms for easier multiplication:
5ln = ln(6 + x)
5ln = (6 * ln + x * ln)
5ln = (6ln + lnx)

Solving
5ln = 6ln + lnx

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.
5ln + -6ln = 6ln + -6ln + lnx

Combine like terms: 5ln + -6ln = -1ln
-1ln = 6ln + -6ln + lnx

Combine like terms: 6ln + -6ln = 0
-1ln = 0 + lnx
-1ln = lnx

Add '-1lnx' to each side of the equation.
-1ln + -1lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
-1ln + -1lnx = 0

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

Ignore the factor -1.

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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