ln(r+5)=ln(4s+2)

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Solution for ln(r+5)=ln(4s+2) equation:


Simplifying
ln(r + 5) = ln(4s + 2)

Reorder the terms:
ln(5 + r) = ln(4s + 2)
(5 * ln + r * ln) = ln(4s + 2)
(5ln + lnr) = ln(4s + 2)

Reorder the terms:
5ln + lnr = ln(2 + 4s)
5ln + lnr = (2 * ln + 4s * ln)
5ln + lnr = (2ln + 4lns)

Solving
5ln + lnr = 2ln + 4lns

Solving for variable 'l'.

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

Add '-2ln' to each side of the equation.
5ln + -2ln + lnr = 2ln + -2ln + 4lns

Combine like terms: 5ln + -2ln = 3ln
3ln + lnr = 2ln + -2ln + 4lns

Combine like terms: 2ln + -2ln = 0
3ln + lnr = 0 + 4lns
3ln + lnr = 4lns

Add '-4lns' to each side of the equation.
3ln + lnr + -4lns = 4lns + -4lns

Combine like terms: 4lns + -4lns = 0
3ln + lnr + -4lns = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(3 + r + -4s) = 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 + r + -4s)' equal to zero and attempt to solve: Simplifying 3 + r + -4s = 0 Solving 3 + r + -4s = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + r + -3 + -4s = 0 + -3 Reorder the terms: 3 + -3 + r + -4s = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r + -4s = 0 + -3 r + -4s = 0 + -3 Combine like terms: 0 + -3 = -3 r + -4s = -3 Add '-1r' to each side of the equation. r + -1r + -4s = -3 + -1r Combine like terms: r + -1r = 0 0 + -4s = -3 + -1r -4s = -3 + -1r Add '4s' to each side of the equation. -4s + 4s = -3 + -1r + 4s Combine like terms: -4s + 4s = 0 0 = -3 + -1r + 4s Simplifying 0 = -3 + -1r + 4s 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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