a*ln(x)-b*ln(y)=a*ln(y)-b*ln(x)

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Solution for a*ln(x)-b*ln(y)=a*ln(y)-b*ln(x) equation: 


Simplifying
a * ln(x) + -1b * ln(y) = a * ln(y) + -1b * ln(x)

Multiply a * ln
aln * x + -1b * ln(y) = a * ln(y) + -1b * ln(x)

Multiply aln * x
alnx + -1b * ln(y) = a * ln(y) + -1b * ln(x)

Multiply b * ln
alnx + -1bln * y = a * ln(y) + -1b * ln(x)

Multiply bln * y
alnx + -1blny = a * ln(y) + -1b * ln(x)

Multiply a * ln
alnx + -1blny = aln * y + -1b * ln(x)

Multiply aln * y
alnx + -1blny = alny + -1b * ln(x)

Multiply b * ln
alnx + -1blny = alny + -1bln * x

Multiply bln * x
alnx + -1blny = alny + -1blnx

Solving
alnx + -1blny = alny + -1blnx

Solving for variable 'a'.

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

Add '-1alny' to each side of the equation.
alnx + -1alny + -1blny = alny + -1alny + -1blnx

Combine like terms: alny + -1alny = 0
alnx + -1alny + -1blny = 0 + -1blnx
alnx + -1alny + -1blny = -1blnx

Add 'blny' to each side of the equation.
alnx + -1alny + -1blny + blny = -1blnx + blny

Combine like terms: -1blny + blny = 0
alnx + -1alny + 0 = -1blnx + blny
alnx + -1alny = -1blnx + blny

Reorder the terms:
alnx + -1alny + blnx + -1blny = -1blnx + blnx + blny + -1blny

Combine like terms: -1blnx + blnx = 0
alnx + -1alny + blnx + -1blny = 0 + blny + -1blny
alnx + -1alny + blnx + -1blny = blny + -1blny

Combine like terms: blny + -1blny = 0
alnx + -1alny + blnx + -1blny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(ax + -1ay + bx + -1by) = 0


Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve:

Simplifying
ln = 0

Solving
ln = 0

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

Add '-1ln' to each side of the equation.
ln + -1ln = 0 + -1ln
Remove the zero:
0 = -1ln

Simplifying
0 = -1ln

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 '(ax + -1ay + bx + -1by)' equal to zero and attempt to solve:

Simplifying
ax + -1ay + bx + -1by = 0

Solving
ax + -1ay + bx + -1by = 0

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

Add '-1bx' to each side of the equation.
ax + -1ay + bx + -1bx + -1by = 0 + -1bx

Combine like terms: bx + -1bx = 0
ax + -1ay + 0 + -1by = 0 + -1bx
ax + -1ay + -1by = 0 + -1bx
Remove the zero:
ax + -1ay + -1by = -1bx

Add 'by' to each side of the equation.
ax + -1ay + -1by + by = -1bx + by

Combine like terms: -1by + by = 0
ax + -1ay + 0 = -1bx + by
ax + -1ay = -1bx + by

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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