ln(5x+12)+ln(2)=2ln(x)

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Solution for ln(5x+12)+ln(2)=2ln(x) equation: 


Simplifying
ln(5x + 12) + ln(2) = 2ln(x)

Reorder the terms:
ln(12 + 5x) + ln(2) = 2ln(x)
(12 * ln + 5x * ln) + ln(2) = 2ln(x)
(12ln + 5lnx) + ln(2) = 2ln(x)

Reorder the terms for easier multiplication:
12ln + 5lnx + 2ln = 2ln(x)

Reorder the terms:
12ln + 2ln + 5lnx = 2ln(x)

Combine like terms: 12ln + 2ln = 14ln
14ln + 5lnx = 2ln(x)

Multiply ln * x
14ln + 5lnx = 2lnx

Solving
14ln + 5lnx = 2lnx

Solving for variable 'l'.

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

Add '-2lnx' to each side of the equation.
14ln + 5lnx + -2lnx = 2lnx + -2lnx

Combine like terms: 5lnx + -2lnx = 3lnx
14ln + 3lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 0
14ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(14 + 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 '(14 + 3x)' equal to zero and attempt to solve:

Simplifying
14 + 3x = 0

Solving
14 + 3x = 0

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

Add '-14' to each side of the equation.
14 + -14 + 3x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 3x = 0 + -14
3x = 0 + -14

Combine like terms: 0 + -14 = -14
3x = -14

Add '-3x' to each side of the equation.
3x + -3x = -14 + -3x

Combine like terms: 3x + -3x = 0
0 = -14 + -3x

Simplifying
0 = -14 + -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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