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Simplifying log(4x + 5) = log(x + 5) + log(3) Reorder the terms: glo(5 + 4x) = log(x + 5) + log(3) (5 * glo + 4x * glo) = log(x + 5) + log(3) (5glo + 4glox) = log(x + 5) + log(3) Reorder the terms: 5glo + 4glox = glo(5 + x) + log(3) 5glo + 4glox = (5 * glo + x * glo) + log(3) 5glo + 4glox = (5glo + glox) + log(3) Reorder the terms for easier multiplication: 5glo + 4glox = 5glo + glox + 3glo Reorder the terms: 5glo + 4glox = 5glo + 3glo + glox Combine like terms: 5glo + 3glo = 8glo 5glo + 4glox = 8glo + glox Solving 5glo + 4glox = 8glo + glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8glo' to each side of the equation. 5glo + -8glo + 4glox = 8glo + -8glo + glox Combine like terms: 5glo + -8glo = -3glo -3glo + 4glox = 8glo + -8glo + glox Combine like terms: 8glo + -8glo = 0 -3glo + 4glox = 0 + glox -3glo + 4glox = glox Add '-1glox' to each side of the equation. -3glo + 4glox + -1glox = glox + -1glox Combine like terms: 4glox + -1glox = 3glox -3glo + 3glox = glox + -1glox Combine like terms: glox + -1glox = 0 -3glo + 3glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(-1 + x) = 0 Ignore the factor 3.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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