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Simplifying log(3x) = log(5) + log(x + -3) Remove parenthesis around (3x) glo * 3x = log(5) + log(x + -3) Reorder the terms for easier multiplication: 3glo * x = log(5) + log(x + -3) Multiply glo * x 3glox = log(5) + log(x + -3) Reorder the terms for easier multiplication: 3glox = 5glo + log(x + -3) Reorder the terms: 3glox = 5glo + glo(-3 + x) 3glox = 5glo + (-3 * glo + x * glo) 3glox = 5glo + (-3glo + glox) Combine like terms: 5glo + -3glo = 2glo 3glox = 2glo + glox Solving 3glox = 2glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-2glo' to each side of the equation. -2glo + 3glox = 2glo + -2glo + glox Combine like terms: 2glo + -2glo = 0 -2glo + 3glox = 0 + glox -2glo + 3glox = glox Add '-1glox' to each side of the equation. -2glo + 3glox + -1glox = glox + -1glox Combine like terms: 3glox + -1glox = 2glox -2glo + 2glox = glox + -1glox Combine like terms: glox + -1glox = 0 -2glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-1 + x) = 0 Ignore the factor 2.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 '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Add '-1x' to each side of the equation. x + -1x = 1 + -1x Combine like terms: x + -1x = 0 0 = 1 + -1x Simplifying 0 = 1 + -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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