4ln(2)+ln(x-2)=ln(96)

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Solution for 4ln(2)+ln(x-2)=ln(96) equation:


Simplifying
4ln(2) + ln(x + -2) = ln(96)

Reorder the terms for easier multiplication:
4 * 2ln + ln(x + -2) = ln(96)

Multiply 4 * 2
8ln + ln(x + -2) = ln(96)

Reorder the terms:
8ln + ln(-2 + x) = ln(96)
8ln + (-2 * ln + x * ln) = ln(96)
8ln + (-2ln + lnx) = ln(96)

Combine like terms: 8ln + -2ln = 6ln
6ln + lnx = ln(96)

Reorder the terms for easier multiplication:
6ln + lnx = 96ln

Solving
6ln + lnx = 96ln

Solving for variable 'l'.

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

Add '-96ln' to each side of the equation.
6ln + -96ln + lnx = 96ln + -96ln

Combine like terms: 6ln + -96ln = -90ln
-90ln + lnx = 96ln + -96ln

Combine like terms: 96ln + -96ln = 0
-90ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-90 + 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 '(-90 + x)' equal to zero and attempt to solve: Simplifying -90 + x = 0 Solving -90 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 0 + 90 Combine like terms: -90 + 90 = 0 0 + x = 0 + 90 x = 0 + 90 Combine like terms: 0 + 90 = 90 x = 90 Add '-1x' to each side of the equation. x + -1x = 90 + -1x Combine like terms: x + -1x = 0 0 = 90 + -1x Simplifying 0 = 90 + -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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