Log(x-5)=log(2x-1)

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Solution for Log(x-5)=log(2x-1) equation:


Simplifying
Log(x + -5) = log(2x + -1)

Reorder the terms:
goL(-5 + x) = log(2x + -1)
(-5 * goL + x * goL) = log(2x + -1)
(-5goL + goxL) = log(2x + -1)

Reorder the terms:
-5goL + goxL = glo(-1 + 2x)
-5goL + goxL = (-1 * glo + 2x * glo)
-5goL + goxL = (-1glo + 2glox)

Solving
-5goL + goxL = -1glo + 2glox

Solving for variable 'g'.

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

Add 'glo' to each side of the equation.
-5goL + glo + goxL = -1glo + glo + 2glox

Reorder the terms:
glo + -5goL + goxL = -1glo + glo + 2glox

Combine like terms: -1glo + glo = 0
glo + -5goL + goxL = 0 + 2glox
glo + -5goL + goxL = 2glox

Add '-2glox' to each side of the equation.
glo + -5goL + -2glox + goxL = 2glox + -2glox

Reorder the terms:
glo + -2glox + -5goL + goxL = 2glox + -2glox

Combine like terms: 2glox + -2glox = 0
glo + -2glox + -5goL + goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(l + -2lx + -5L + xL) = 0

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 + -2lx + -5L + xL)' equal to zero and attempt to solve: Simplifying l + -2lx + -5L + xL = 0 Reorder the terms: -5L + l + -2lx + xL = 0 Solving -5L + l + -2lx + xL = 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 + -2lx + 5L + xL = 0 + 5L Reorder the terms: -5L + 5L + l + -2lx + xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + l + -2lx + xL = 0 + 5L l + -2lx + xL = 0 + 5L Remove the zero: l + -2lx + xL = 5L Add '-1l' to each side of the equation. l + -2lx + -1l + xL = 5L + -1l Reorder the terms: l + -1l + -2lx + xL = 5L + -1l Combine like terms: l + -1l = 0 0 + -2lx + xL = 5L + -1l -2lx + xL = 5L + -1l Add '2lx' to each side of the equation. -2lx + 2lx + xL = 5L + -1l + 2lx Combine like terms: -2lx + 2lx = 0 0 + xL = 5L + -1l + 2lx xL = 5L + -1l + 2lx Add '-1xL' to each side of the equation. xL + -1xL = 5L + -1l + 2lx + -1xL Combine like terms: xL + -1xL = 0 0 = 5L + -1l + 2lx + -1xL Simplifying 0 = 5L + -1l + 2lx + -1xL 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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