ln(4x+1)=ln(3x+5)

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Solution for ln(4x+1)=ln(3x+5) equation:


Simplifying
ln(4x + 1) = ln(3x + 5)

Reorder the terms:
ln(1 + 4x) = ln(3x + 5)
(1 * ln + 4x * ln) = ln(3x + 5)
(1ln + 4lnx) = ln(3x + 5)

Reorder the terms:
1ln + 4lnx = ln(5 + 3x)
1ln + 4lnx = (5 * ln + 3x * ln)
1ln + 4lnx = (5ln + 3lnx)

Solving
1ln + 4lnx = 5ln + 3lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
1ln + -5ln + 4lnx = 5ln + -5ln + 3lnx

Combine like terms: 1ln + -5ln = -4ln
-4ln + 4lnx = 5ln + -5ln + 3lnx

Combine like terms: 5ln + -5ln = 0
-4ln + 4lnx = 0 + 3lnx
-4ln + 4lnx = 3lnx

Add '-3lnx' to each side of the equation.
-4ln + 4lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 4lnx + -3lnx = 1lnx
-4ln + 1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
-4ln + 1lnx = 0

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

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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