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Simplifying log(5) + log(x + 3) = log(4x + 20) Reorder the terms for easier multiplication: 5glo + log(x + 3) = log(4x + 20) Reorder the terms: 5glo + glo(3 + x) = log(4x + 20) 5glo + (3 * glo + x * glo) = log(4x + 20) 5glo + (3glo + glox) = log(4x + 20) Combine like terms: 5glo + 3glo = 8glo 8glo + glox = log(4x + 20) Reorder the terms: 8glo + glox = glo(20 + 4x) 8glo + glox = (20 * glo + 4x * glo) 8glo + glox = (20glo + 4glox) Solving 8glo + glox = 20glo + 4glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-20glo' to each side of the equation. 8glo + -20glo + glox = 20glo + -20glo + 4glox Combine like terms: 8glo + -20glo = -12glo -12glo + glox = 20glo + -20glo + 4glox Combine like terms: 20glo + -20glo = 0 -12glo + glox = 0 + 4glox -12glo + glox = 4glox Add '-4glox' to each side of the equation. -12glo + glox + -4glox = 4glox + -4glox Combine like terms: glox + -4glox = -3glox -12glo + -3glox = 4glox + -4glox Combine like terms: 4glox + -4glox = 0 -12glo + -3glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(4 + 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 '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -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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