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Simplifying log(5x + 3) = log(x + 5) + log(4) Reorder the terms: glo(3 + 5x) = log(x + 5) + log(4) (3 * glo + 5x * glo) = log(x + 5) + log(4) (3glo + 5glox) = log(x + 5) + log(4) Reorder the terms: 3glo + 5glox = glo(5 + x) + log(4) 3glo + 5glox = (5 * glo + x * glo) + log(4) 3glo + 5glox = (5glo + glox) + log(4) Reorder the terms for easier multiplication: 3glo + 5glox = 5glo + glox + 4glo Reorder the terms: 3glo + 5glox = 5glo + 4glo + glox Combine like terms: 5glo + 4glo = 9glo 3glo + 5glox = 9glo + glox Solving 3glo + 5glox = 9glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glo' to each side of the equation. 3glo + -9glo + 5glox = 9glo + -9glo + glox Combine like terms: 3glo + -9glo = -6glo -6glo + 5glox = 9glo + -9glo + glox Combine like terms: 9glo + -9glo = 0 -6glo + 5glox = 0 + glox -6glo + 5glox = glox Add '-1glox' to each side of the equation. -6glo + 5glox + -1glox = glox + -1glox Combine like terms: 5glox + -1glox = 4glox -6glo + 4glox = glox + -1glox Combine like terms: glox + -1glox = 0 -6glo + 4glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-3 + 2x) = 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 '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Add '-2x' to each side of the equation. 2x + -2x = 3 + -2x Combine like terms: 2x + -2x = 0 0 = 3 + -2x Simplifying 0 = 3 + -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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