Log(9)(x+2)=log(9)(3x+5)

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Solution for Log(9)(x+2)=log(9)(3x+5) equation:


Simplifying
Log(9)(x + 2) = log(9)(3x + 5)

Reorder the terms:
goL * 9(2 + x) = log(9)(3x + 5)

Reorder the terms for easier multiplication:
9goL(2 + x) = log(9)(3x + 5)
(2 * 9goL + x * 9goL) = log(9)(3x + 5)
(18goL + 9goxL) = log(9)(3x + 5)

Reorder the terms:
18goL + 9goxL = glo * 9(5 + 3x)

Reorder the terms for easier multiplication:
18goL + 9goxL = 9glo(5 + 3x)
18goL + 9goxL = (5 * 9glo + 3x * 9glo)
18goL + 9goxL = (45glo + 27glox)

Solving
18goL + 9goxL = 45glo + 27glox

Solving for variable 'g'.

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

Add '-45glo' to each side of the equation.
18goL + -45glo + 9goxL = 45glo + -45glo + 27glox

Reorder the terms:
-45glo + 18goL + 9goxL = 45glo + -45glo + 27glox

Combine like terms: 45glo + -45glo = 0
-45glo + 18goL + 9goxL = 0 + 27glox
-45glo + 18goL + 9goxL = 27glox

Add '-27glox' to each side of the equation.
-45glo + 18goL + -27glox + 9goxL = 27glox + -27glox

Reorder the terms:
-45glo + -27glox + 18goL + 9goxL = 27glox + -27glox

Combine like terms: 27glox + -27glox = 0
-45glo + -27glox + 18goL + 9goxL = 0

Factor out the Greatest Common Factor (GCF), '9go'.
9go(-5l + -3lx + 2L + xL) = 0

Ignore the factor 9.

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 '(-5l + -3lx + 2L + xL)' equal to zero and attempt to solve: Simplifying -5l + -3lx + 2L + xL = 0 Reorder the terms: 2L + -5l + -3lx + xL = 0 Solving 2L + -5l + -3lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-2L' to each side of the equation. 2L + -5l + -3lx + -2L + xL = 0 + -2L Reorder the terms: 2L + -2L + -5l + -3lx + xL = 0 + -2L Combine like terms: 2L + -2L = 0 0 + -5l + -3lx + xL = 0 + -2L -5l + -3lx + xL = 0 + -2L Remove the zero: -5l + -3lx + xL = -2L Add '5l' to each side of the equation. -5l + -3lx + 5l + xL = -2L + 5l Reorder the terms: -5l + 5l + -3lx + xL = -2L + 5l Combine like terms: -5l + 5l = 0 0 + -3lx + xL = -2L + 5l -3lx + xL = -2L + 5l Add '3lx' to each side of the equation. -3lx + 3lx + xL = -2L + 5l + 3lx Combine like terms: -3lx + 3lx = 0 0 + xL = -2L + 5l + 3lx xL = -2L + 5l + 3lx Add '-1xL' to each side of the equation. xL + -1xL = -2L + 5l + 3lx + -1xL Combine like terms: xL + -1xL = 0 0 = -2L + 5l + 3lx + -1xL Simplifying 0 = -2L + 5l + 3lx + -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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