ln(5x-1)=ln(2x+8)

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Solution for ln(5x-1)=ln(2x+8) equation:


Simplifying
ln(5x + -1) = ln(2x + 8)

Reorder the terms:
ln(-1 + 5x) = ln(2x + 8)
(-1 * ln + 5x * ln) = ln(2x + 8)
(-1ln + 5lnx) = ln(2x + 8)

Reorder the terms:
-1ln + 5lnx = ln(8 + 2x)
-1ln + 5lnx = (8 * ln + 2x * ln)
-1ln + 5lnx = (8ln + 2lnx)

Solving
-1ln + 5lnx = 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.
-1ln + -8ln + 5lnx = 8ln + -8ln + 2lnx

Combine like terms: -1ln + -8ln = -9ln
-9ln + 5lnx = 8ln + -8ln + 2lnx

Combine like terms: 8ln + -8ln = 0
-9ln + 5lnx = 0 + 2lnx
-9ln + 5lnx = 2lnx

Add '-2lnx' to each side of the equation.
-9ln + 5lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 5lnx + -2lnx = 3lnx
-9ln + 3lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
-9ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), '3ln'.
3ln(-3 + x) = 0

Ignore the factor 3.

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 '(-3 + x)' equal to zero and attempt to solve: Simplifying -3 + x = 0 Solving -3 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0 + 3 x = 0 + 3 Combine like terms: 0 + 3 = 3 x = 3 Add '-1x' to each side of the equation. x + -1x = 3 + -1x Combine like terms: x + -1x = 0 0 = 3 + -1x Simplifying 0 = 3 + -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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