log(4x)=log(3x-5)

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Solution for log(4x)=log(3x-5) equation:


Simplifying
log(4x) = log(3x + -5)

Remove parenthesis around (4x)
glo * 4x = log(3x + -5)

Reorder the terms for easier multiplication:
4glo * x = log(3x + -5)

Multiply glo * x
4glox = log(3x + -5)

Reorder the terms:
4glox = glo(-5 + 3x)
4glox = (-5 * glo + 3x * glo)
4glox = (-5glo + 3glox)

Solving
4glox = -5glo + 3glox

Solving for variable 'g'.

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

Add '5glo' to each side of the equation.
5glo + 4glox = -5glo + 5glo + 3glox

Combine like terms: -5glo + 5glo = 0
5glo + 4glox = 0 + 3glox
5glo + 4glox = 3glox

Add '-3glox' to each side of the equation.
5glo + 4glox + -3glox = 3glox + -3glox

Combine like terms: 4glox + -3glox = 1glox
5glo + 1glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
5glo + 1glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(5 + x) = 0

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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