ln(x)+ln(3)=ln(12)

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Solution for ln(x)+ln(3)=ln(12) equation: 


Simplifying
ln(x) + ln(3) = ln(12)

Multiply ln * x
lnx + ln(3) = ln(12)

Reorder the terms for easier multiplication:
lnx + 3ln = ln(12)

Reorder the terms:
3ln + lnx = ln(12)

Reorder the terms for easier multiplication:
3ln + lnx = 12ln

Solving
3ln + lnx = 12ln

Solving for variable 'l'.

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

Add '-12ln' to each side of the equation.
3ln + -12ln + lnx = 12ln + -12ln

Combine like terms: 3ln + -12ln = -9ln
-9ln + lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-9ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-9 + x) = 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 '(-9 + x)' equal to zero and attempt to solve:

Simplifying
-9 + x = 0

Solving
-9 + x = 0

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

Add '9' to each side of the equation.
-9 + 9 + x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + x = 0 + 9
x = 0 + 9

Combine like terms: 0 + 9 = 9
x = 9

Add '-1x' to each side of the equation.
x + -1x = 9 + -1x

Combine like terms: x + -1x = 0
0 = 9 + -1x

Simplifying
0 = 9 + -1x

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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