ln(2)-ln(5-x)=ln(62)

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Solution for ln(2)-ln(5-x)=ln(62) equation:


Simplifying
ln(2) + -1ln(5 + -1x) = ln(62)

Reorder the terms for easier multiplication:
2ln + -1ln(5 + -1x) = ln(62)
2ln + (5 * -1ln + -1x * -1ln) = ln(62)
2ln + (-5ln + 1lnx) = ln(62)

Combine like terms: 2ln + -5ln = -3ln
-3ln + 1lnx = ln(62)

Reorder the terms for easier multiplication:
-3ln + 1lnx = 62ln

Solving
-3ln + 1lnx = 62ln

Solving for variable 'l'.

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

Add '-62ln' to each side of the equation.
-3ln + -62ln + 1lnx = 62ln + -62ln

Combine like terms: -3ln + -62ln = -65ln
-65ln + 1lnx = 62ln + -62ln

Combine like terms: 62ln + -62ln = 0
-65ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-65 + x) = 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 '(-65 + x)' equal to zero and attempt to solve: Simplifying -65 + x = 0 Solving -65 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 0 + 65 Combine like terms: -65 + 65 = 0 0 + x = 0 + 65 x = 0 + 65 Combine like terms: 0 + 65 = 65 x = 65 Add '-1x' to each side of the equation. x + -1x = 65 + -1x Combine like terms: x + -1x = 0 0 = 65 + -1x Simplifying 0 = 65 + -1x 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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