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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