ln-3x=ln(4x+7)

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Solution for ln-3x=ln(4x+7) equation: 


Simplifying
ln + -3x = ln(4x + 7)

Reorder the terms:
ln + -3x = ln(7 + 4x)
ln + -3x = (7 * ln + 4x * ln)
ln + -3x = (7ln + 4lnx)

Solving
ln + -3x = 7ln + 4lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
ln + -7ln + -3x = 7ln + -7ln + 4lnx

Combine like terms: ln + -7ln = -6ln
-6ln + -3x = 7ln + -7ln + 4lnx

Combine like terms: 7ln + -7ln = 0
-6ln + -3x = 0 + 4lnx
-6ln + -3x = 4lnx

Add '-4lnx' to each side of the equation.
-6ln + -4lnx + -3x = 4lnx + -4lnx

Combine like terms: 4lnx + -4lnx = 0
-6ln + -4lnx + -3x = 0

Add '3x' to each side of the equation.
-6ln + -4lnx + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
-6ln + -4lnx + 0 = 0 + 3x
-6ln + -4lnx = 0 + 3x
Remove the zero:
-6ln + -4lnx = 3x

Combine like terms: 3x + -3x = 0
-6ln + -4lnx + -3x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6ln + 4lnx + 3x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6ln + 4lnx + 3x)' equal to zero and attempt to solve:

Simplifying
6ln + 4lnx + 3x = 0

Solving
6ln + 4lnx + 3x = 0

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

Add '-3x' to each side of the equation.
6ln + 4lnx + 3x + -3x = 0 + -3x

Combine like terms: 3x + -3x = 0
6ln + 4lnx + 0 = 0 + -3x
6ln + 4lnx = 0 + -3x
Remove the zero:
6ln + 4lnx = -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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