ln(32)-ln(x)=ln(2x)

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Solution for ln(32)-ln(x)=ln(2x) equation: 


Simplifying
ln(32) + -1ln(x) = ln(2x)

Reorder the terms for easier multiplication:
32ln + -1ln(x) = ln(2x)

Multiply ln * x
32ln + -1lnx = ln(2x)

Remove parenthesis around (2x)
32ln + -1lnx = ln * 2x

Reorder the terms for easier multiplication:
32ln + -1lnx = 2ln * x

Multiply ln * x
32ln + -1lnx = 2lnx

Solving
32ln + -1lnx = 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.
32ln + -1lnx + -2lnx = 2lnx + -2lnx

Combine like terms: -1lnx + -2lnx = -3lnx
32ln + -3lnx = 2lnx + -2lnx

Combine like terms: 2lnx + -2lnx = 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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