ln(x-2)-ln(9)=ln(15)

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Solution for ln(x-2)-ln(9)=ln(15) equation:


Simplifying
ln(x + -2) + -1ln(9) = ln(15)

Reorder the terms:
ln(-2 + x) + -1ln(9) = ln(15)
(-2 * ln + x * ln) + -1ln(9) = ln(15)
(-2ln + lnx) + -1ln(9) = ln(15)

Reorder the terms for easier multiplication:
-2ln + lnx + -1 * 9ln = ln(15)

Multiply -1 * 9
-2ln + lnx + -9ln = ln(15)

Reorder the terms:
-2ln + -9ln + lnx = ln(15)

Combine like terms: -2ln + -9ln = -11ln
-11ln + lnx = ln(15)

Reorder the terms for easier multiplication:
-11ln + lnx = 15ln

Solving
-11ln + lnx = 15ln

Solving for variable 'l'.

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

Add '-15ln' to each side of the equation.
-11ln + -15ln + lnx = 15ln + -15ln

Combine like terms: -11ln + -15ln = -26ln
-26ln + lnx = 15ln + -15ln

Combine like terms: 15ln + -15ln = 0
-26ln + lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-26 + 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 '(-26 + x)' equal to zero and attempt to solve: Simplifying -26 + x = 0 Solving -26 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + x = 0 + 26 x = 0 + 26 Combine like terms: 0 + 26 = 26 x = 26 Add '-1x' to each side of the equation. x + -1x = 26 + -1x Combine like terms: x + -1x = 0 0 = 26 + -1x Simplifying 0 = 26 + -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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