ln(2x)+ln(x-2)=ln(30)

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Solution for ln(2x)+ln(x-2)=ln(30) equation: 


Simplifying
ln(2x) + ln(x + -2) = ln(30)

Remove parenthesis around (2x)
ln * 2x + ln(x + -2) = ln(30)

Reorder the terms for easier multiplication:
2ln * x + ln(x + -2) = ln(30)

Multiply ln * x
2lnx + ln(x + -2) = ln(30)

Reorder the terms:
2lnx + ln(-2 + x) = ln(30)
2lnx + (-2 * ln + x * ln) = ln(30)
2lnx + (-2ln + lnx) = ln(30)

Reorder the terms:
-2ln + 2lnx + lnx = ln(30)

Combine like terms: 2lnx + lnx = 3lnx
-2ln + 3lnx = ln(30)

Reorder the terms for easier multiplication:
-2ln + 3lnx = 30ln

Solving
-2ln + 3lnx = 30ln

Solving for variable 'l'.

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

Add '-30ln' to each side of the equation.
-2ln + -30ln + 3lnx = 30ln + -30ln

Combine like terms: -2ln + -30ln = -32ln
-32ln + 3lnx = 30ln + -30ln

Combine like terms: 30ln + -30ln = 0
-32ln + 3lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-32 + 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 '(-32 + 3x)' equal to zero and attempt to solve:

Simplifying
-32 + 3x = 0

Solving
-32 + 3x = 0

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

Add '32' to each side of the equation.
-32 + 32 + 3x = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 3x = 0 + 32
3x = 0 + 32

Combine like terms: 0 + 32 = 32
3x = 32

Add '-3x' to each side of the equation.
3x + -3x = 32 + -3x

Combine like terms: 3x + -3x = 0
0 = 32 + -3x

Simplifying
0 = 32 + -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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