ln(10)-ln(2x)-2x=0

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Solution for ln(10)-ln(2x)-2x=0 equation: 


Simplifying
ln(10) + -1ln(2x) + -2x = 0

Reorder the terms for easier multiplication:
10ln + -1ln(2x) + -2x = 0

Remove parenthesis around (2x)
10ln + -1ln * 2x + -2x = 0

Reorder the terms for easier multiplication:
10ln + -1 * 2ln * x + -2x = 0

Multiply -1 * 2
10ln + -2ln * x + -2x = 0

Multiply ln * x
10ln + -2lnx + -2x = 0

Solving
10ln + -2lnx + -2x = 0

Solving for variable 'l'.

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

Add '2x' to each side of the equation.
10ln + -2lnx + -2x + 2x = 0 + 2x

Combine like terms: -2x + 2x = 0
10ln + -2lnx + 0 = 0 + 2x
10ln + -2lnx = 0 + 2x
Remove the zero:
10ln + -2lnx = 2x

Combine like terms: 2x + -2x = 0
10ln + -2lnx + -2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5ln + -1lnx + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5ln + -1lnx + -1x)' equal to zero and attempt to solve:

Simplifying
5ln + -1lnx + -1x = 0

Solving
5ln + -1lnx + -1x = 0

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

Add 'x' to each side of the equation.
5ln + -1lnx + -1x + x = 0 + x

Combine like terms: -1x + x = 0
5ln + -1lnx + 0 = 0 + x
5ln + -1lnx = 0 + x
Remove the zero:
5ln + -1lnx = 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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