log[3](5x-1)=log[3](x+7)

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Solution for log[3](5x-1)=log[3](x+7) equation:


Simplifying
log[3](5x + -1) = log[3](x + 7)

Reorder the terms:
glo * 3(-1 + 5x) = log[3](x + 7)

Reorder the terms for easier multiplication:
3glo(-1 + 5x) = log[3](x + 7)
(-1 * 3glo + 5x * 3glo) = log[3](x + 7)
(-3glo + 15glox) = log[3](x + 7)

Reorder the terms:
-3glo + 15glox = glo * 3(7 + x)

Reorder the terms for easier multiplication:
-3glo + 15glox = 3glo(7 + x)
-3glo + 15glox = (7 * 3glo + x * 3glo)
-3glo + 15glox = (21glo + 3glox)

Solving
-3glo + 15glox = 21glo + 3glox

Solving for variable 'g'.

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

Add '-21glo' to each side of the equation.
-3glo + -21glo + 15glox = 21glo + -21glo + 3glox

Combine like terms: -3glo + -21glo = -24glo
-24glo + 15glox = 21glo + -21glo + 3glox

Combine like terms: 21glo + -21glo = 0
-24glo + 15glox = 0 + 3glox
-24glo + 15glox = 3glox

Add '-3glox' to each side of the equation.
-24glo + 15glox + -3glox = 3glox + -3glox

Combine like terms: 15glox + -3glox = 12glox
-24glo + 12glox = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
-24glo + 12glox = 0

Factor out the Greatest Common Factor (GCF), '12glo'.
12glo(-2 + x) = 0

Ignore the factor 12.

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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -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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