2ln(x+3)=ln(5x+29)

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Solution for 2ln(x+3)=ln(5x+29) equation:


Simplifying
2ln(x + 3) = ln(5x + 29)

Reorder the terms:
2ln(3 + x) = ln(5x + 29)
(3 * 2ln + x * 2ln) = ln(5x + 29)
(6ln + 2lnx) = ln(5x + 29)

Reorder the terms:
6ln + 2lnx = ln(29 + 5x)
6ln + 2lnx = (29 * ln + 5x * ln)
6ln + 2lnx = (29ln + 5lnx)

Solving
6ln + 2lnx = 29ln + 5lnx

Solving for variable 'l'.

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

Add '-29ln' to each side of the equation.
6ln + -29ln + 2lnx = 29ln + -29ln + 5lnx

Combine like terms: 6ln + -29ln = -23ln
-23ln + 2lnx = 29ln + -29ln + 5lnx

Combine like terms: 29ln + -29ln = 0
-23ln + 2lnx = 0 + 5lnx
-23ln + 2lnx = 5lnx

Add '-5lnx' to each side of the equation.
-23ln + 2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
-23ln + -3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
-23ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(23 + 3x) = 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 '(23 + 3x)' equal to zero and attempt to solve: Simplifying 23 + 3x = 0 Solving 23 + 3x = 0 Move all terms containing l to the left, all other terms to the right. Add '-23' to each side of the equation. 23 + -23 + 3x = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 3x = 0 + -23 3x = 0 + -23 Combine like terms: 0 + -23 = -23 3x = -23 Add '-3x' to each side of the equation. 3x + -3x = -23 + -3x Combine like terms: 3x + -3x = 0 0 = -23 + -3x Simplifying 0 = -23 + -3x 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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