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Simplifying log(4x + 1) + log(5) = log(19x + 20) Reorder the terms: glo(1 + 4x) + log(5) = log(19x + 20) (1 * glo + 4x * glo) + log(5) = log(19x + 20) (1glo + 4glox) + log(5) = log(19x + 20) Reorder the terms for easier multiplication: 1glo + 4glox + 5glo = log(19x + 20) Reorder the terms: 1glo + 5glo + 4glox = log(19x + 20) Combine like terms: 1glo + 5glo = 6glo 6glo + 4glox = log(19x + 20) Reorder the terms: 6glo + 4glox = glo(20 + 19x) 6glo + 4glox = (20 * glo + 19x * glo) 6glo + 4glox = (20glo + 19glox) Solving 6glo + 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. 6glo + -20glo + 4glox = 20glo + -20glo + 19glox Combine like terms: 6glo + -20glo = -14glo -14glo + 4glox = 20glo + -20glo + 19glox Combine like terms: 20glo + -20glo = 0 -14glo + 4glox = 0 + 19glox -14glo + 4glox = 19glox Add '-19glox' to each side of the equation. -14glo + 4glox + -19glox = 19glox + -19glox Combine like terms: 4glox + -19glox = -15glox -14glo + -15glox = 19glox + -19glox Combine like terms: 19glox + -19glox = 0 -14glo + -15glox = 0 Factor out the Greatest Common Factor (GCF), '-1glo'. -1glo(14 + 15x) = 0 Ignore the factor -1.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 '(14 + 15x)' equal to zero and attempt to solve: Simplifying 14 + 15x = 0 Solving 14 + 15x = 0 Move all terms containing g to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 15x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 15x = 0 + -14 15x = 0 + -14 Combine like terms: 0 + -14 = -14 15x = -14 Add '-15x' to each side of the equation. 15x + -15x = -14 + -15x Combine like terms: 15x + -15x = 0 0 = -14 + -15x Simplifying 0 = -14 + -15x 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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