ln(5x)-ln(2)=ln(20)

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Solution for ln(5x)-ln(2)=ln(20) equation: 


Simplifying
ln(5x) + -1ln(2) = ln(20)

Remove parenthesis around (5x)
ln * 5x + -1ln(2) = ln(20)

Reorder the terms for easier multiplication:
5ln * x + -1ln(2) = ln(20)

Multiply ln * x
5lnx + -1ln(2) = ln(20)

Reorder the terms for easier multiplication:
5lnx + -1 * 2ln = ln(20)

Multiply -1 * 2
5lnx + -2ln = ln(20)

Reorder the terms:
-2ln + 5lnx = ln(20)

Reorder the terms for easier multiplication:
-2ln + 5lnx = 20ln

Solving
-2ln + 5lnx = 20ln

Solving for variable 'l'.

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

Add '-20ln' to each side of the equation.
-2ln + -20ln + 5lnx = 20ln + -20ln

Combine like terms: -2ln + -20ln = -22ln
-22ln + 5lnx = 20ln + -20ln

Combine like terms: 20ln + -20ln = 0
-22ln + 5lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-22 + 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 '(-22 + 5x)' equal to zero and attempt to solve:

Simplifying
-22 + 5x = 0

Solving
-22 + 5x = 0

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

Add '22' to each side of the equation.
-22 + 22 + 5x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + 5x = 0 + 22
5x = 0 + 22

Combine like terms: 0 + 22 = 22
5x = 22

Add '-5x' to each side of the equation.
5x + -5x = 22 + -5x

Combine like terms: 5x + -5x = 0
0 = 22 + -5x

Simplifying
0 = 22 + -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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