Log(9x+2)=log(38x-6)-log(x+7)

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Solution for Log(9x+2)=log(38x-6)-log(x+7) equation:


Simplifying
Log(9x + 2) = log(38x + -6) + -1log(x + 7)

Reorder the terms:
goL(2 + 9x) = log(38x + -6) + -1log(x + 7)
(2 * goL + 9x * goL) = log(38x + -6) + -1log(x + 7)
(2goL + 9goxL) = log(38x + -6) + -1log(x + 7)

Reorder the terms:
2goL + 9goxL = glo(-6 + 38x) + -1log(x + 7)
2goL + 9goxL = (-6 * glo + 38x * glo) + -1log(x + 7)
2goL + 9goxL = (-6glo + 38glox) + -1log(x + 7)

Reorder the terms:
2goL + 9goxL = -6glo + 38glox + -1glo(7 + x)
2goL + 9goxL = -6glo + 38glox + (7 * -1glo + x * -1glo)
2goL + 9goxL = -6glo + 38glox + (-7glo + -1glox)

Reorder the terms:
2goL + 9goxL = -6glo + -7glo + 38glox + -1glox

Combine like terms: -6glo + -7glo = -13glo
2goL + 9goxL = -13glo + 38glox + -1glox

Combine like terms: 38glox + -1glox = 37glox
2goL + 9goxL = -13glo + 37glox

Solving
2goL + 9goxL = -13glo + 37glox

Solving for variable 'g'.

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

Add '13glo' to each side of the equation.
2goL + 13glo + 9goxL = -13glo + 13glo + 37glox

Reorder the terms:
13glo + 2goL + 9goxL = -13glo + 13glo + 37glox

Combine like terms: -13glo + 13glo = 0
13glo + 2goL + 9goxL = 0 + 37glox
13glo + 2goL + 9goxL = 37glox

Add '-37glox' to each side of the equation.
13glo + 2goL + -37glox + 9goxL = 37glox + -37glox

Reorder the terms:
13glo + -37glox + 2goL + 9goxL = 37glox + -37glox

Combine like terms: 37glox + -37glox = 0
13glo + -37glox + 2goL + 9goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(13l + -37lx + 2L + 9xL) = 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 '(13l + -37lx + 2L + 9xL)' equal to zero and attempt to solve: Simplifying 13l + -37lx + 2L + 9xL = 0 Reorder the terms: 2L + 13l + -37lx + 9xL = 0 Solving 2L + 13l + -37lx + 9xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-2L' to each side of the equation. 2L + 13l + -37lx + -2L + 9xL = 0 + -2L Reorder the terms: 2L + -2L + 13l + -37lx + 9xL = 0 + -2L Combine like terms: 2L + -2L = 0 0 + 13l + -37lx + 9xL = 0 + -2L 13l + -37lx + 9xL = 0 + -2L Remove the zero: 13l + -37lx + 9xL = -2L Add '-13l' to each side of the equation. 13l + -37lx + -13l + 9xL = -2L + -13l Reorder the terms: 13l + -13l + -37lx + 9xL = -2L + -13l Combine like terms: 13l + -13l = 0 0 + -37lx + 9xL = -2L + -13l -37lx + 9xL = -2L + -13l Add '37lx' to each side of the equation. -37lx + 37lx + 9xL = -2L + -13l + 37lx Combine like terms: -37lx + 37lx = 0 0 + 9xL = -2L + -13l + 37lx 9xL = -2L + -13l + 37lx Add '-9xL' to each side of the equation. 9xL + -9xL = -2L + -13l + 37lx + -9xL Combine like terms: 9xL + -9xL = 0 0 = -2L + -13l + 37lx + -9xL Simplifying 0 = -2L + -13l + 37lx + -9xL 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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