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

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


Simplifying
2ln(5) + -1ln(x) = ln(2)

Reorder the terms for easier multiplication:
2 * 5ln + -1ln(x) = ln(2)

Multiply 2 * 5
10ln + -1ln(x) = ln(2)

Multiply ln * x
10ln + -1lnx = ln(2)

Reorder the terms for easier multiplication:
10ln + -1lnx = 2ln

Solving
10ln + -1lnx = 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.
10ln + -2ln + -1lnx = 2ln + -2ln

Combine like terms: 10ln + -2ln = 8ln
8ln + -1lnx = 2ln + -2ln

Combine like terms: 2ln + -2ln = 0
8ln + -1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Add 'x' to each side of the equation.
-1x + x = -8 + x

Combine like terms: -1x + x = 0
0 = -8 + x

Simplifying
0 = -8 + x

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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