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

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


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

Multiply ln * x
2lnx = ln(2) + ln(5x + -12)

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

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

Combine like terms: 2ln + -12ln = -10ln
2lnx = -10ln + 5lnx

Solving
2lnx = -10ln + 5lnx

Solving for variable 'l'.

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

Add '10ln' to each side of the equation.
10ln + 2lnx = -10ln + 10ln + 5lnx

Combine like terms: -10ln + 10ln = 0
10ln + 2lnx = 0 + 5lnx
10ln + 2lnx = 5lnx

Add '-5lnx' to each side of the equation.
10ln + 2lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 2lnx + -5lnx = -3lnx
10ln + -3lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
10ln + -3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(10 + -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 '(10 + -3x)' equal to zero and attempt to solve:

Simplifying
10 + -3x = 0

Solving
10 + -3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x = 0 + -10
-3x = 0 + -10

Combine like terms: 0 + -10 = -10
-3x = -10

Add '3x' to each side of the equation.
-3x + 3x = -10 + 3x

Combine like terms: -3x + 3x = 0
0 = -10 + 3x

Simplifying
0 = -10 + 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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