ln(x^2)=ln(5)+ln(8)-ln(10)

Solution for ln(x^2)=ln(5)+ln(8)-ln(10) equation:

Simplifying
ln(x2) = ln(5) + ln(8) + -1ln(10)

Multiply ln * x2
lnx2 = ln(5) + ln(8) + -1ln(10)

Reorder the terms for easier multiplication:
lnx2 = 5ln + ln(8) + -1ln(10)

Reorder the terms for easier multiplication:
lnx2 = 5ln + 8ln + -1ln(10)

Reorder the terms for easier multiplication:
lnx2 = 5ln + 8ln + -1 * 10ln

Multiply -1 * 10
lnx2 = 5ln + 8ln + -10ln

Combine like terms: 5ln + 8ln = 13ln
lnx2 = 13ln + -10ln

Combine like terms: 13ln + -10ln = 3ln
lnx2 = 3ln

Solving
lnx2 = 3ln

Solving for variable 'l'.

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

Add '-3ln' to each side of the equation.
-3ln + lnx2 = 3ln + -3ln

Combine like terms: 3ln + -3ln = 0
-3ln + lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-3 + x2) = 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 '(-3 + x2)' equal to zero and attempt to solve:

Simplifying
-3 + x2 = 0

Solving
-3 + x2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x2 = 0 + 3
x2 = 0 + 3

Combine like terms: 0 + 3 = 3
x2 = 3

Add '-1x2' to each side of the equation.
x2 + -1x2 = 3 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 3 + -1x2

Simplifying
0 = 3 + -1x2

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.