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Simplifying log(10x) = log(3x + 14) Remove parenthesis around (10x) glo * 10x = log(3x + 14) Reorder the terms for easier multiplication: 10glo * x = log(3x + 14) Multiply glo * x 10glox = log(3x + 14) Reorder the terms: 10glox = glo(14 + 3x) 10glox = (14 * glo + 3x * glo) 10glox = (14glo + 3glox) Solving 10glox = 14glo + 3glox 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 + 10glox = 14glo + -14glo + 3glox Combine like terms: 14glo + -14glo = 0 -14glo + 10glox = 0 + 3glox -14glo + 10glox = 3glox Add '-3glox' to each side of the equation. -14glo + 10glox + -3glox = 3glox + -3glox Combine like terms: 10glox + -3glox = 7glox -14glo + 7glox = 3glox + -3glox Combine like terms: 3glox + -3glox = 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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