Log(x-5)+logx=log(x-9)

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Solution for Log(x-5)+logx=log(x-9) equation:


Simplifying
Log(x + -5) + logx = log(x + -9)

Reorder the terms:
goL(-5 + x) + logx = log(x + -9)
(-5 * goL + x * goL) + logx = log(x + -9)
(-5goL + goxL) + logx = log(x + -9)

Reorder the terms:
glox + -5goL + goxL = log(x + -9)

Reorder the terms:
glox + -5goL + goxL = glo(-9 + x)
glox + -5goL + goxL = (-9 * glo + x * glo)
glox + -5goL + goxL = (-9glo + glox)

Add '-1glox' to each side of the equation.
glox + -5goL + -1glox + goxL = -9glo + glox + -1glox

Reorder the terms:
glox + -1glox + -5goL + goxL = -9glo + glox + -1glox

Combine like terms: glox + -1glox = 0
0 + -5goL + goxL = -9glo + glox + -1glox
-5goL + goxL = -9glo + glox + -1glox

Combine like terms: glox + -1glox = 0
-5goL + goxL = -9glo + 0
-5goL + goxL = -9glo

Solving
-5goL + goxL = -9glo

Solving for variable 'g'.

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

Add '9glo' to each side of the equation.
-5goL + 9glo + goxL = -9glo + 9glo

Reorder the terms:
9glo + -5goL + goxL = -9glo + 9glo

Combine like terms: -9glo + 9glo = 0
9glo + -5goL + goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(9l + -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 '(9l + -5L + xL)' equal to zero and attempt to solve: Simplifying 9l + -5L + xL = 0 Reorder the terms: -5L + 9l + xL = 0 Solving -5L + 9l + 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 + 9l + 5L + xL = 0 + 5L Reorder the terms: -5L + 5L + 9l + xL = 0 + 5L Combine like terms: -5L + 5L = 0 0 + 9l + xL = 0 + 5L 9l + xL = 0 + 5L Remove the zero: 9l + xL = 5L Add '-9l' to each side of the equation. 9l + -9l + xL = 5L + -9l Combine like terms: 9l + -9l = 0 0 + xL = 5L + -9l xL = 5L + -9l Add '-1xL' to each side of the equation. xL + -1xL = 5L + -9l + -1xL Combine like terms: xL + -1xL = 0 0 = 5L + -9l + -1xL Simplifying 0 = 5L + -9l + -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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