2lnx=ln(3x+4)

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Solution for 2lnx=ln(3x+4) equation:


Simplifying
2lnx = ln(3x + 4)

Reorder the terms:
2lnx = ln(4 + 3x)
2lnx = (4 * ln + 3x * ln)
2lnx = (4ln + 3lnx)

Solving
2lnx = 4ln + 3lnx

Solving for variable 'l'.

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

Add '-4ln' to each side of the equation.
-4ln + 2lnx = 4ln + -4ln + 3lnx

Combine like terms: 4ln + -4ln = 0
-4ln + 2lnx = 0 + 3lnx
-4ln + 2lnx = 3lnx

Add '-3lnx' to each side of the equation.
-4ln + 2lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 2lnx + -3lnx = -1lnx
-4ln + -1lnx = 3lnx + -3lnx

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

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