ln(3-5x)-2ln(x)=ln(2)

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Solution for ln(3-5x)-2ln(x)=ln(2) equation: 


Simplifying
ln(3 + -5x) + -2ln(x) = ln(2)
(3 * ln + -5x * ln) + -2ln(x) = ln(2)
(3ln + -5lnx) + -2ln(x) = ln(2)

Multiply ln * x
3ln + -5lnx + -2lnx = ln(2)

Combine like terms: -5lnx + -2lnx = -7lnx
3ln + -7lnx = ln(2)

Reorder the terms for easier multiplication:
3ln + -7lnx = 2ln

Solving
3ln + -7lnx = 2ln

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
3ln + -2ln + -7lnx = 2ln + -2ln

Combine like terms: 3ln + -2ln = 1ln
1ln + -7lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
1ln + -7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(1 + -7x) = 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 '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Add '7x' to each side of the equation.
-7x + 7x = -1 + 7x

Combine like terms: -7x + 7x = 0
0 = -1 + 7x

Simplifying
0 = -1 + 7x

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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