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Simplifying log(2x) = log(7x + -10) Remove parenthesis around (2x) glo * 2x = log(7x + -10) Reorder the terms for easier multiplication: 2glo * x = log(7x + -10) Multiply glo * x 2glox = log(7x + -10) Reorder the terms: 2glox = glo(-10 + 7x) 2glox = (-10 * glo + 7x * glo) 2glox = (-10glo + 7glox) Solving 2glox = -10glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '10glo' to each side of the equation. 10glo + 2glox = -10glo + 10glo + 7glox Combine like terms: -10glo + 10glo = 0 10glo + 2glox = 0 + 7glox 10glo + 2glox = 7glox Add '-7glox' to each side of the equation. 10glo + 2glox + -7glox = 7glox + -7glox Combine like terms: 2glox + -7glox = -5glox 10glo + -5glox = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 10glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(2 + -1x) = 0 Ignore the factor 5.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 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + x 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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