Ln(4x+5)=Ln(2x+27)

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Solution for Ln(4x+5)=Ln(2x+27) equation:


Simplifying
Ln(4x + 5) = Ln(2x + 27)

Reorder the terms:
nL(5 + 4x) = Ln(2x + 27)
(5 * nL + 4x * nL) = Ln(2x + 27)
(5nL + 4nxL) = Ln(2x + 27)

Reorder the terms:
5nL + 4nxL = nL(27 + 2x)
5nL + 4nxL = (27 * nL + 2x * nL)
5nL + 4nxL = (27nL + 2nxL)

Solving
5nL + 4nxL = 27nL + 2nxL

Solving for variable 'n'.

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

Add '-27nL' to each side of the equation.
5nL + -27nL + 4nxL = 27nL + -27nL + 2nxL

Combine like terms: 5nL + -27nL = -22nL
-22nL + 4nxL = 27nL + -27nL + 2nxL

Combine like terms: 27nL + -27nL = 0
-22nL + 4nxL = 0 + 2nxL
-22nL + 4nxL = 2nxL

Add '-2nxL' to each side of the equation.
-22nL + 4nxL + -2nxL = 2nxL + -2nxL

Combine like terms: 4nxL + -2nxL = 2nxL
-22nL + 2nxL = 2nxL + -2nxL

Combine like terms: 2nxL + -2nxL = 0
-22nL + 2nxL = 0

Factor out the Greatest Common Factor (GCF), '2nL'.
2nL(-11 + x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'nL' equal to zero and attempt to solve: Simplifying nL = 0 Solving nL = 0 Move all terms containing n to the left, all other terms to the right. Simplifying nL = 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 '(-11 + x)' equal to zero and attempt to solve: Simplifying -11 + x = 0 Solving -11 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x = 0 + 11 x = 0 + 11 Combine like terms: 0 + 11 = 11 x = 11 Add '-1x' to each side of the equation. x + -1x = 11 + -1x Combine like terms: x + -1x = 0 0 = 11 + -1x Simplifying 0 = 11 + -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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