Log(3)(5x-5)-log(3)(x-1)=0

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Solution for Log(3)(5x-5)-log(3)(x-1)=0 equation:


Simplifying
Log(3)(5x + -5) + -1log(3)(x + -1) = 0

Reorder the terms:
goL * 3(-5 + 5x) + -1log(3)(x + -1) = 0

Reorder the terms for easier multiplication:
3goL(-5 + 5x) + -1log(3)(x + -1) = 0
(-5 * 3goL + 5x * 3goL) + -1log(3)(x + -1) = 0
(-15goL + 15goxL) + -1log(3)(x + -1) = 0

Reorder the terms:
-15goL + 15goxL + -1glo * 3(-1 + x) = 0

Reorder the terms for easier multiplication:
-15goL + 15goxL + -1 * 3glo(-1 + x) = 0

Multiply -1 * 3
-15goL + 15goxL + -3glo(-1 + x) = 0
-15goL + 15goxL + (-1 * -3glo + x * -3glo) = 0
-15goL + 15goxL + (3glo + -3glox) = 0

Reorder the terms:
3glo + -3glox + -15goL + 15goxL = 0

Solving
3glo + -3glox + -15goL + 15goxL = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), '3go'.
3go(l + -1lx + -5L + 5xL) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(l + -1lx + -5L + 5xL)' equal to zero and attempt to solve: Simplifying l + -1lx + -5L + 5xL = 0 Reorder the terms: -5L + l + -1lx + 5xL = 0 Solving -5L + l + -1lx + 5xL = 0 Move all terms containing g to the left, all other terms to the right. Add '5L' to each side of the equation. -5L + l + -1lx + 5L + 5xL = 0 + 5L Reorder the terms: -5L + 5L + l + -1lx + 5xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + l + -1lx + 5xL = 0 + 5L l + -1lx + 5xL = 0 + 5L Remove the zero: l + -1lx + 5xL = 5L Add '-1l' to each side of the equation. l + -1lx + -1l + 5xL = 5L + -1l Reorder the terms: l + -1l + -1lx + 5xL = 5L + -1l Combine like terms: l + -1l = 0 0 + -1lx + 5xL = 5L + -1l -1lx + 5xL = 5L + -1l Add 'lx' to each side of the equation. -1lx + lx + 5xL = 5L + -1l + lx Combine like terms: -1lx + lx = 0 0 + 5xL = 5L + -1l + lx 5xL = 5L + -1l + lx Add '-5xL' to each side of the equation. 5xL + -5xL = 5L + -1l + lx + -5xL Combine like terms: 5xL + -5xL = 0 0 = 5L + -1l + lx + -5xL Simplifying 0 = 5L + -1l + lx + -5xL 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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