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Simplifying log(3)(5x + 13) + -1log(3) * 6 = log(3) * 3x Reorder the terms: glo * 3(13 + 5x) + -1log(3) * 6 = log(3) * 3x Reorder the terms for easier multiplication: 3glo(13 + 5x) + -1log(3) * 6 = log(3) * 3x (13 * 3glo + 5x * 3glo) + -1log(3) * 6 = log(3) * 3x (39glo + 15glox) + -1log(3) * 6 = log(3) * 3x Reorder the terms for easier multiplication: 39glo + 15glox + -1 * 3 * 6glo = log(3) * 3x Multiply -1 * 3 39glo + 15glox + -3 * 6glo = log(3) * 3x Multiply -3 * 6 39glo + 15glox + -18glo = log(3) * 3x Reorder the terms: 39glo + -18glo + 15glox = log(3) * 3x Combine like terms: 39glo + -18glo = 21glo 21glo + 15glox = log(3) * 3x Reorder the terms for easier multiplication: 21glo + 15glox = 3 * 3glo * x Multiply 3 * 3 21glo + 15glox = 9glo * x Multiply glo * x 21glo + 15glox = 9glox Solving 21glo + 15glox = 9glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-9glox' to each side of the equation. 21glo + 15glox + -9glox = 9glox + -9glox Combine like terms: 15glox + -9glox = 6glox 21glo + 6glox = 9glox + -9glox Combine like terms: 9glox + -9glox = 0 21glo + 6glox = 0 Factor out the Greatest Common Factor (GCF), '3glo'. 3glo(7 + 2x) = 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 '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Add '-2x' to each side of the equation. 2x + -2x = -7 + -2x Combine like terms: 2x + -2x = 0 0 = -7 + -2x Simplifying 0 = -7 + -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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