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Simplifying log(4x + 3) + log(5) = log(19x + 20) Reorder the terms: glo(3 + 4x) + log(5) = log(19x + 20) (3 * glo + 4x * glo) + log(5) = log(19x + 20) (3glo + 4glox) + log(5) = log(19x + 20) Reorder the terms for easier multiplication: 3glo + 4glox + 5glo = log(19x + 20) Reorder the terms: 3glo + 5glo + 4glox = log(19x + 20) Combine like terms: 3glo + 5glo = 8glo 8glo + 4glox = log(19x + 20) Reorder the terms: 8glo + 4glox = glo(20 + 19x) 8glo + 4glox = (20 * glo + 19x * glo) 8glo + 4glox = (20glo + 19glox) Solving 8glo + 4glox = 20glo + 19glox 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 + 4glox = 20glo + -20glo + 19glox Combine like terms: 8glo + -20glo = -12glo -12glo + 4glox = 20glo + -20glo + 19glox Combine like terms: 20glo + -20glo = 0 -12glo + 4glox = 0 + 19glox -12glo + 4glox = 19glox Add '-19glox' to each side of the equation. -12glo + 4glox + -19glox = 19glox + -19glox Combine like terms: 4glox + -19glox = -15glox -12glo + -15glox = 19glox + -19glox Combine like terms: 19glox + -19glox = 0 -12glo + -15glox = 0 Factor out the Greatest Common Factor (GCF), '-3glo'. -3glo(4 + 5x) = 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 + 5x)' equal to zero and attempt to solve: Simplifying 4 + 5x = 0 Solving 4 + 5x = 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 + 5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5x = 0 + -4 5x = 0 + -4 Combine like terms: 0 + -4 = -4 5x = -4 Add '-5x' to each side of the equation. 5x + -5x = -4 + -5x Combine like terms: 5x + -5x = 0 0 = -4 + -5x Simplifying 0 = -4 + -5x 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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