ln(5y)=ln(7x)

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Solution for ln(5y)=ln(7x) equation: 


Simplifying
ln(5y) = ln(7x)

Remove parenthesis around (5y)
ln * 5y = ln(7x)

Reorder the terms for easier multiplication:
5ln * y = ln(7x)

Multiply ln * y
5lny = ln(7x)

Remove parenthesis around (7x)
5lny = ln * 7x

Reorder the terms for easier multiplication:
5lny = 7ln * x

Multiply ln * x
5lny = 7lnx

Solving
5lny = 7lnx

Solving for variable 'l'.

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

Add '-7lnx' to each side of the equation.
-7lnx + 5lny = 7lnx + -7lnx

Combine like terms: 7lnx + -7lnx = 0
-7lnx + 5lny = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7x + 5y) = 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 '(-7x + 5y)' equal to zero and attempt to solve:

Simplifying
-7x + 5y = 0

Solving
-7x + 5y = 0

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

Add '7x' to each side of the equation.
-7x + 7x + 5y = 0 + 7x

Combine like terms: -7x + 7x = 0
0 + 5y = 0 + 7x
5y = 0 + 7x
Remove the zero:
5y = 7x

Add '-5y' to each side of the equation.
5y + -5y = 7x + -5y

Combine like terms: 5y + -5y = 0
0 = 7x + -5y

Simplifying
0 = 7x + -5y

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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