51ln(1-x)=ln(1-46x)

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Solution for 51ln(1-x)=ln(1-46x) equation:


Simplifying
51ln(1 + -1x) = ln(1 + -46x)
(1 * 51ln + -1x * 51ln) = ln(1 + -46x)
(51ln + -51lnx) = ln(1 + -46x)
51ln + -51lnx = (1 * ln + -46x * ln)
51ln + -51lnx = (1ln + -46lnx)

Solving
51ln + -51lnx = 1ln + -46lnx

Solving for variable 'l'.

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

Add '-1ln' to each side of the equation.
51ln + -1ln + -51lnx = 1ln + -1ln + -46lnx

Combine like terms: 51ln + -1ln = 50ln
50ln + -51lnx = 1ln + -1ln + -46lnx

Combine like terms: 1ln + -1ln = 0
50ln + -51lnx = 0 + -46lnx
50ln + -51lnx = -46lnx

Add '46lnx' to each side of the equation.
50ln + -51lnx + 46lnx = -46lnx + 46lnx

Combine like terms: -51lnx + 46lnx = -5lnx
50ln + -5lnx = -46lnx + 46lnx

Combine like terms: -46lnx + 46lnx = 0
50ln + -5lnx = 0

Factor out the Greatest Common Factor (GCF), '5ln'.
5ln(10 + -1x) = 0

Ignore the factor 5.

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 '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Add 'x' to each side of the equation. -1x + x = -10 + x Combine like terms: -1x + x = 0 0 = -10 + x Simplifying 0 = -10 + x 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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