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

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


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

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

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

Solving
5glo + glox = -4glo + 4glox

Solving for variable 'g'.

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

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

Combine like terms: 5glo + 4glo = 9glo
9glo + glox = -4glo + 4glo + 4glox

Combine like terms: -4glo + 4glo = 0
9glo + glox = 0 + 4glox
9glo + glox = 4glox

Add '-4glox' to each side of the equation.
9glo + glox + -4glox = 4glox + -4glox

Combine like terms: glox + -4glox = -3glox
9glo + -3glox = 4glox + -4glox

Combine like terms: 4glox + -4glox = 0
9glo + -3glox = 0

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

Ignore the factor 3.

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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing g 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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