ln(2x)+ln(3)=ln(24)

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Solution for ln(2x)+ln(3)=ln(24) equation: 


Simplifying
ln(2x) + ln(3) = ln(24)

Remove parenthesis around (2x)
ln * 2x + ln(3) = ln(24)

Reorder the terms for easier multiplication:
2ln * x + ln(3) = ln(24)

Multiply ln * x
2lnx + ln(3) = ln(24)

Reorder the terms for easier multiplication:
2lnx + 3ln = ln(24)

Reorder the terms:
3ln + 2lnx = ln(24)

Reorder the terms for easier multiplication:
3ln + 2lnx = 24ln

Solving
3ln + 2lnx = 24ln

Solving for variable 'l'.

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

Add '-24ln' to each side of the equation.
3ln + -24ln + 2lnx = 24ln + -24ln

Combine like terms: 3ln + -24ln = -21ln
-21ln + 2lnx = 24ln + -24ln

Combine like terms: 24ln + -24ln = 0
-21ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-21 + 2x) = 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 '(-21 + 2x)' equal to zero and attempt to solve:

Simplifying
-21 + 2x = 0

Solving
-21 + 2x = 0

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

Add '21' to each side of the equation.
-21 + 21 + 2x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + 2x = 0 + 21
2x = 0 + 21

Combine like terms: 0 + 21 = 21
2x = 21

Add '-2x' to each side of the equation.
2x + -2x = 21 + -2x

Combine like terms: 2x + -2x = 0
0 = 21 + -2x

Simplifying
0 = 21 + -2x

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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