(2x+16)ln(2)=(x-27)ln(3)

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Solution for (2x+16)ln(2)=(x-27)ln(3) equation:


Simplifying
(2x + 16) * ln(2) = (x + -27) * ln(3)

Reorder the terms:
(16 + 2x) * ln(2) = (x + -27) * ln(3)

Reorder the terms for easier multiplication:
2ln(16 + 2x) = (x + -27) * ln(3)
(16 * 2ln + 2x * 2ln) = (x + -27) * ln(3)
(32ln + 4lnx) = (x + -27) * ln(3)

Reorder the terms:
32ln + 4lnx = (-27 + x) * ln(3)

Reorder the terms for easier multiplication:
32ln + 4lnx = 3ln(-27 + x)
32ln + 4lnx = (-27 * 3ln + x * 3ln)
32ln + 4lnx = (-81ln + 3lnx)

Solving
32ln + 4lnx = -81ln + 3lnx

Solving for variable 'l'.

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

Add '81ln' to each side of the equation.
32ln + 81ln + 4lnx = -81ln + 81ln + 3lnx

Combine like terms: 32ln + 81ln = 113ln
113ln + 4lnx = -81ln + 81ln + 3lnx

Combine like terms: -81ln + 81ln = 0
113ln + 4lnx = 0 + 3lnx
113ln + 4lnx = 3lnx

Add '-3lnx' to each side of the equation.
113ln + 4lnx + -3lnx = 3lnx + -3lnx

Combine like terms: 4lnx + -3lnx = 1lnx
113ln + 1lnx = 3lnx + -3lnx

Combine like terms: 3lnx + -3lnx = 0
113ln + 1lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(113 + 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 '(113 + x)' equal to zero and attempt to solve: Simplifying 113 + x = 0 Solving 113 + x = 0 Move all terms containing l to the left, all other terms to the right. Add '-113' to each side of the equation. 113 + -113 + x = 0 + -113 Combine like terms: 113 + -113 = 0 0 + x = 0 + -113 x = 0 + -113 Combine like terms: 0 + -113 = -113 x = -113 Add '-1x' to each side of the equation. x + -1x = -113 + -1x Combine like terms: x + -1x = 0 0 = -113 + -1x Simplifying 0 = -113 + -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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