ln(x-23)-In(5-x)=In(4)+In(x)

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Solution for ln(x-23)-In(5-x)=In(4)+In(x) equation:


Simplifying
ln(x + -23) + -1In(5 + -1x) = In(4) + In(x)

Reorder the terms:
ln(-23 + x) + -1In(5 + -1x) = In(4) + In(x)
(-23 * ln + x * ln) + -1In(5 + -1x) = In(4) + In(x)
(-23ln + lnx) + -1In(5 + -1x) = In(4) + In(x)
-23ln + lnx + (5 * -1nI + -1x * -1nI) = In(4) + In(x)
-23ln + lnx + (-5nI + 1nxI) = In(4) + In(x)

Reorder the terms for easier multiplication:
-23ln + lnx + -5nI + 1nxI = 4nI + In(x)

Multiply nI * x
-23ln + lnx + -5nI + 1nxI = 4nI + nxI

Solving
-23ln + lnx + -5nI + 1nxI = 4nI + nxI

Solving for variable 'l'.

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

Add '5nI' to each side of the equation.
-23ln + lnx + -5nI + 5nI + 1nxI = 4nI + 5nI + nxI

Combine like terms: -5nI + 5nI = 0
-23ln + lnx + 0 + 1nxI = 4nI + 5nI + nxI
-23ln + lnx + 1nxI = 4nI + 5nI + nxI

Combine like terms: 4nI + 5nI = 9nI
-23ln + lnx + 1nxI = 9nI + nxI

Add '-1nxI' to each side of the equation.
-23ln + lnx + 1nxI + -1nxI = 9nI + nxI + -1nxI

Combine like terms: 1nxI + -1nxI = 0
-23ln + lnx + 0 = 9nI + nxI + -1nxI
-23ln + lnx = 9nI + nxI + -1nxI

Combine like terms: nxI + -1nxI = 0
-23ln + lnx = 9nI + 0
-23ln + lnx = 9nI

Combine like terms: 9nI + -9nI = 0
-23ln + lnx + -9nI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-23l + lx + -9I) = 0

Subproblem 1

Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing l to the left, all other terms to the right. Add '-1n' to each side of the equation. n + -1n = 0 + -1n Remove the zero: 0 = -1n Simplifying 0 = -1n 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 '(-23l + lx + -9I)' equal to zero and attempt to solve: Simplifying -23l + lx + -9I = 0 Reorder the terms: -9I + -23l + lx = 0 Solving -9I + -23l + lx = 0 Move all terms containing l to the left, all other terms to the right. Add '9I' to each side of the equation. -9I + -23l + 9I + lx = 0 + 9I Reorder the terms: -9I + 9I + -23l + lx = 0 + 9I Combine like terms: -9I + 9I = 0 0 + -23l + lx = 0 + 9I -23l + lx = 0 + 9I Remove the zero: -23l + lx = 9I 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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