4xln(3)=(x-1)ln(5)

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Solution for 4xln(3)=(x-1)ln(5) equation:


Simplifying
4xln(3) = (x + -1) * ln(5)

Reorder the terms for easier multiplication:
4 * 3lnx = (x + -1) * ln(5)

Multiply 4 * 3
12lnx = (x + -1) * ln(5)

Reorder the terms:
12lnx = (-1 + x) * ln(5)

Reorder the terms for easier multiplication:
12lnx = 5ln(-1 + x)
12lnx = (-1 * 5ln + x * 5ln)
12lnx = (-5ln + 5lnx)

Solving
12lnx = -5ln + 5lnx

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
5ln + 12lnx = -5ln + 5ln + 5lnx

Combine like terms: -5ln + 5ln = 0
5ln + 12lnx = 0 + 5lnx
5ln + 12lnx = 5lnx

Add '-5lnx' to each side of the equation.
5ln + 12lnx + -5lnx = 5lnx + -5lnx

Combine like terms: 12lnx + -5lnx = 7lnx
5ln + 7lnx = 5lnx + -5lnx

Combine like terms: 5lnx + -5lnx = 0
5ln + 7lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(5 + 7x) = 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 '(5 + 7x)' equal to zero and attempt to solve: Simplifying 5 + 7x = 0 Solving 5 + 7x = 0 Move all terms containing l to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x = 0 + -5 7x = 0 + -5 Combine like terms: 0 + -5 = -5 7x = -5 Add '-7x' to each side of the equation. 7x + -7x = -5 + -7x Combine like terms: 7x + -7x = 0 0 = -5 + -7x Simplifying 0 = -5 + -7x 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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