ln(12x+7)+ln(x)=ln(12)

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Solution for ln(12x+7)+ln(x)=ln(12) equation: 


Simplifying
ln(12x + 7) + ln(x) = ln(12)

Reorder the terms:
ln(7 + 12x) + ln(x) = ln(12)
(7 * ln + 12x * ln) + ln(x) = ln(12)
(7ln + 12lnx) + ln(x) = ln(12)

Multiply ln * x
7ln + 12lnx + lnx = ln(12)

Combine like terms: 12lnx + lnx = 13lnx
7ln + 13lnx = ln(12)

Reorder the terms for easier multiplication:
7ln + 13lnx = 12ln

Solving
7ln + 13lnx = 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.
7ln + -12ln + 13lnx = 12ln + -12ln

Combine like terms: 7ln + -12ln = -5ln
-5ln + 13lnx = 12ln + -12ln

Combine like terms: 12ln + -12ln = 0
-5ln + 13lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + 13x) = 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 '(-5 + 13x)' equal to zero and attempt to solve:

Simplifying
-5 + 13x = 0

Solving
-5 + 13x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 13x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 13x = 0 + 5
13x = 0 + 5

Combine like terms: 0 + 5 = 5
13x = 5

Add '-13x' to each side of the equation.
13x + -13x = 5 + -13x

Combine like terms: 13x + -13x = 0
0 = 5 + -13x

Simplifying
0 = 5 + -13x

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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