logx+log(x+14)=log(4x-21)

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Solution for logx+log(x+14)=log(4x-21) equation:


Simplifying
logx + log(x + 14) = log(4x + -21)

Reorder the terms:
glox + glo(14 + x) = log(4x + -21)
glox + (14 * glo + x * glo) = log(4x + -21)
glox + (14glo + glox) = log(4x + -21)

Reorder the terms:
14glo + glox + glox = log(4x + -21)

Combine like terms: glox + glox = 2glox
14glo + 2glox = log(4x + -21)

Reorder the terms:
14glo + 2glox = glo(-21 + 4x)
14glo + 2glox = (-21 * glo + 4x * glo)
14glo + 2glox = (-21glo + 4glox)

Solving
14glo + 2glox = -21glo + 4glox

Solving for variable 'g'.

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

Add '21glo' to each side of the equation.
14glo + 21glo + 2glox = -21glo + 21glo + 4glox

Combine like terms: 14glo + 21glo = 35glo
35glo + 2glox = -21glo + 21glo + 4glox

Combine like terms: -21glo + 21glo = 0
35glo + 2glox = 0 + 4glox
35glo + 2glox = 4glox

Add '-4glox' to each side of the equation.
35glo + 2glox + -4glox = 4glox + -4glox

Combine like terms: 2glox + -4glox = -2glox
35glo + -2glox = 4glox + -4glox

Combine like terms: 4glox + -4glox = 0
35glo + -2glox = 0

Factor out the Greatest Common Factor (GCF), 'glo'.
glo(35 + -2x) = 0

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(35 + -2x)' equal to zero and attempt to solve: Simplifying 35 + -2x = 0 Solving 35 + -2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-35' to each side of the equation. 35 + -35 + -2x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -2x = 0 + -35 -2x = 0 + -35 Combine like terms: 0 + -35 = -35 -2x = -35 Add '2x' to each side of the equation. -2x + 2x = -35 + 2x Combine like terms: -2x + 2x = 0 0 = -35 + 2x Simplifying 0 = -35 + 2x 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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