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

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Solution for ln(3x+1)+ln(2x-3)=ln(10) equation: 


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

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

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

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

Combine like terms: 1ln + -3ln = -2ln
-2ln + 3lnx + 2lnx = ln(10)

Combine like terms: 3lnx + 2lnx = 5lnx
-2ln + 5lnx = ln(10)

Reorder the terms for easier multiplication:
-2ln + 5lnx = 10ln

Solving
-2ln + 5lnx = 10ln

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
-2ln + -10ln + 5lnx = 10ln + -10ln

Combine like terms: -2ln + -10ln = -12ln
-12ln + 5lnx = 10ln + -10ln

Combine like terms: 10ln + -10ln = 0
-12ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-12 + 5x) = 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 '(-12 + 5x)' equal to zero and attempt to solve:

Simplifying
-12 + 5x = 0

Solving
-12 + 5x = 0

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

Add '12' to each side of the equation.
-12 + 12 + 5x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 5x = 0 + 12
5x = 0 + 12

Combine like terms: 0 + 12 = 12
5x = 12

Add '-5x' to each side of the equation.
5x + -5x = 12 + -5x

Combine like terms: 5x + -5x = 0
0 = 12 + -5x

Simplifying
0 = 12 + -5x

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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