ln(5x-8)-2ln(x)=ln(2)

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Solution for ln(5x-8)-2ln(x)=ln(2) equation: 


Simplifying
ln(5x + -8) + -2ln(x) = ln(2)

Reorder the terms:
ln(-8 + 5x) + -2ln(x) = ln(2)
(-8 * ln + 5x * ln) + -2ln(x) = ln(2)
(-8ln + 5lnx) + -2ln(x) = ln(2)

Multiply ln * x
-8ln + 5lnx + -2lnx = ln(2)

Combine like terms: 5lnx + -2lnx = 3lnx
-8ln + 3lnx = ln(2)

Reorder the terms for easier multiplication:
-8ln + 3lnx = 2ln

Solving
-8ln + 3lnx = 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.
-8ln + -2ln + 3lnx = 2ln + -2ln

Combine like terms: -8ln + -2ln = -10ln
-10ln + 3lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 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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