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

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

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

Multiply ln * x
lnx = 2[ln(2) + -1ln(5)]

Reorder the terms for easier multiplication:
lnx = 2[2ln + -1ln(5)]

Reorder the terms for easier multiplication:
lnx = 2[2ln + -1 * 5ln]

Multiply -1 * 5
lnx = 2[2ln + -5ln]

Combine like terms: 2ln + -5ln = -3ln
lnx = 2[-3ln]

Remove brackets around [-3ln]
lnx = 2 * -3ln

Multiply 2 * -3
lnx = -6ln

Solving
lnx = -6ln

Solving for variable 'l'.

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

Add '6ln' to each side of the equation.
6ln + lnx = -6ln + 6ln

Combine like terms: -6ln + 6ln = 0
6ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Add '-1x' to each side of the equation.
x + -1x = -6 + -1x

Combine like terms: x + -1x = 0
0 = -6 + -1x

Simplifying
0 = -6 + -1x

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.