ln(3x-2)=ln(5)

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


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

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

Reorder the terms for easier multiplication:
-2ln + 3lnx = 5ln

Solving
-2ln + 3lnx = 5ln

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.
-2ln + -5ln + 3lnx = 5ln + -5ln

Combine like terms: -2ln + -5ln = -7ln
-7ln + 3lnx = 5ln + -5ln

Combine like terms: 5ln + -5ln = 0
-7ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 3x) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
-7 + 3x = 0

Solving
-7 + 3x = 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 + 3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 3x = 0 + 7
3x = 0 + 7

Combine like terms: 0 + 7 = 7
3x = 7

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

Combine like terms: 3x + -3x = 0
0 = 7 + -3x

Simplifying
0 = 7 + -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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