ln(3x-2)=ln(10)-ln(x-5)

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Solution for ln(3x-2)=ln(10)-ln(x-5) equation: 


Simplifying
ln(3x + -2) = ln(10) + -1ln(x + -5)

Reorder the terms:
ln(-2 + 3x) = ln(10) + -1ln(x + -5)
(-2 * ln + 3x * ln) = ln(10) + -1ln(x + -5)
(-2ln + 3lnx) = ln(10) + -1ln(x + -5)

Reorder the terms for easier multiplication:
-2ln + 3lnx = 10ln + -1ln(x + -5)

Reorder the terms:
-2ln + 3lnx = 10ln + -1ln(-5 + x)
-2ln + 3lnx = 10ln + (-5 * -1ln + x * -1ln)
-2ln + 3lnx = 10ln + (5ln + -1lnx)

Combine like terms: 10ln + 5ln = 15ln
-2ln + 3lnx = 15ln + -1lnx

Solving
-2ln + 3lnx = 15ln + -1lnx

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-2ln + -15ln + 3lnx = 15ln + -15ln + -1lnx

Combine like terms: -2ln + -15ln = -17ln
-17ln + 3lnx = 15ln + -15ln + -1lnx

Combine like terms: 15ln + -15ln = 0
-17ln + 3lnx = 0 + -1lnx
-17ln + 3lnx = -1lnx

Add 'lnx' to each side of the equation.
-17ln + 3lnx + lnx = -1lnx + lnx

Combine like terms: 3lnx + lnx = 4lnx
-17ln + 4lnx = -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-17ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-17 + 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 '(-17 + 4x)' equal to zero and attempt to solve:

Simplifying
-17 + 4x = 0

Solving
-17 + 4x = 0

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

Add '17' to each side of the equation.
-17 + 17 + 4x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 4x = 0 + 17
4x = 0 + 17

Combine like terms: 0 + 17 = 17
4x = 17

Add '-4x' to each side of the equation.
4x + -4x = 17 + -4x

Combine like terms: 4x + -4x = 0
0 = 17 + -4x

Simplifying
0 = 17 + -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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