2log(x)=log(14-5x)

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Solution for 2log(x)=log(14-5x) equation:


Simplifying
2log(x) = log(14 + -5x)

Multiply glo * x
2glox = log(14 + -5x)
2glox = (14 * glo + -5x * glo)
2glox = (14glo + -5glox)

Solving
2glox = 14glo + -5glox

Solving for variable 'g'.

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

Add '-14glo' to each side of the equation.
-14glo + 2glox = 14glo + -14glo + -5glox

Combine like terms: 14glo + -14glo = 0
-14glo + 2glox = 0 + -5glox
-14glo + 2glox = -5glox

Add '5glox' to each side of the equation.
-14glo + 2glox + 5glox = -5glox + 5glox

Combine like terms: 2glox + 5glox = 7glox
-14glo + 7glox = -5glox + 5glox

Combine like terms: -5glox + 5glox = 0
-14glo + 7glox = 0

Factor out the Greatest Common Factor (GCF), '7glo'.
7glo(-2 + x) = 0

Ignore the factor 7.

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