(x)(ln(9))=(x-2)(ln(27))

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Solution for (x)(ln(9))=(x-2)(ln(27)) equation:


Simplifying
(x)(ln(9)) = (x + -2)(ln(27))

Reorder the terms for easier multiplication:
x(9ln) = (x + -2)(ln(27))

Remove parenthesis around (9ln)
x * 9ln = (x + -2)(ln(27))

Reorder the terms for easier multiplication:
9x * ln = (x + -2)(ln(27))

Multiply x * ln
9lnx = (x + -2)(ln(27))

Reorder the terms:
9lnx = (-2 + x)(ln(27))

Reorder the terms for easier multiplication:
9lnx = (-2 + x)(27ln)

Remove parenthesis around (27ln)
9lnx = (-2 + x) * 27ln

Reorder the terms for easier multiplication:
9lnx = 27ln(-2 + x)
9lnx = (-2 * 27ln + x * 27ln)
9lnx = (-54ln + 27lnx)

Solving
9lnx = -54ln + 27lnx

Solving for variable 'l'.

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

Add '54ln' to each side of the equation.
54ln + 9lnx = -54ln + 54ln + 27lnx

Combine like terms: -54ln + 54ln = 0
54ln + 9lnx = 0 + 27lnx
54ln + 9lnx = 27lnx

Add '-27lnx' to each side of the equation.
54ln + 9lnx + -27lnx = 27lnx + -27lnx

Combine like terms: 9lnx + -27lnx = -18lnx
54ln + -18lnx = 27lnx + -27lnx

Combine like terms: 27lnx + -27lnx = 0
54ln + -18lnx = 0

Factor out the Greatest Common Factor (GCF), '18ln'.
18ln(3 + -1x) = 0

Ignore the factor 18.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing l to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Add 'x' to each side of the equation. -1x + x = -3 + x Combine like terms: -1x + x = 0 0 = -3 + x Simplifying 0 = -3 + 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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