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

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


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

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

Reorder the terms for easier multiplication:
5glo(5 + x) = 4log(5)(x + -4)
(5 * 5glo + x * 5glo) = 4log(5)(x + -4)
(25glo + 5glox) = 4log(5)(x + -4)

Reorder the terms:
25glo + 5glox = 4glo * 5(-4 + x)

Reorder the terms for easier multiplication:
25glo + 5glox = 4 * 5glo(-4 + x)

Multiply 4 * 5
25glo + 5glox = 20glo(-4 + x)
25glo + 5glox = (-4 * 20glo + x * 20glo)
25glo + 5glox = (-80glo + 20glox)

Solving
25glo + 5glox = -80glo + 20glox

Solving for variable 'g'.

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

Add '80glo' to each side of the equation.
25glo + 80glo + 5glox = -80glo + 80glo + 20glox

Combine like terms: 25glo + 80glo = 105glo
105glo + 5glox = -80glo + 80glo + 20glox

Combine like terms: -80glo + 80glo = 0
105glo + 5glox = 0 + 20glox
105glo + 5glox = 20glox

Add '-20glox' to each side of the equation.
105glo + 5glox + -20glox = 20glox + -20glox

Combine like terms: 5glox + -20glox = -15glox
105glo + -15glox = 20glox + -20glox

Combine like terms: 20glox + -20glox = 0
105glo + -15glox = 0

Factor out the Greatest Common Factor (GCF), '15glo'.
15glo(7 + -1x) = 0

Ignore the factor 15.

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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + 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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