ln(7-3x)=lnx

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


Simplifying
ln(7 + -3x) = lnx
(7 * ln + -3x * ln) = lnx
(7ln + -3lnx) = lnx

Solving
7ln + -3lnx = lnx

Solving for variable 'l'.

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

Add '-1lnx' to each side of the equation.
7ln + -3lnx + -1lnx = lnx + -1lnx

Combine like terms: -3lnx + -1lnx = -4lnx
7ln + -4lnx = lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
7ln + -4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(7 + -4x) = 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 '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

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

Combine like terms: -4x + 4x = 0
0 = -7 + 4x

Simplifying
0 = -7 + 4x

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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