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

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


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

Remove parenthesis around (2x)
ln * 2x + ln(x + -5) = ln(3)

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

Multiply ln * x
2lnx + ln(x + -5) = ln(3)

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

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

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

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

Solving
-5ln + 3lnx = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-5ln + -3ln + 3lnx = 3ln + -3ln

Combine like terms: -5ln + -3ln = -8ln
-8ln + 3lnx = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-8ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + 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 '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Add '-3x' to each side of the equation.
3x + -3x = 8 + -3x

Combine like terms: 3x + -3x = 0
0 = 8 + -3x

Simplifying
0 = 8 + -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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