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Simplifying log[5](4x2) + -3log[5](2x) = 12 + -1log[5](12x2) Remove parenthesis around (4x2) glo * 5 * 4x2 + -3log[5](2x) = 12 + -1log[5](12x2) Reorder the terms for easier multiplication: 5 * 4glo * x2 + -3log[5](2x) = 12 + -1log[5](12x2) Multiply 5 * 4 20glo * x2 + -3log[5](2x) = 12 + -1log[5](12x2) Multiply glo * x2 20glox2 + -3log[5](2x) = 12 + -1log[5](12x2) Remove parenthesis around (2x) 20glox2 + -3glo * 5 * 2x = 12 + -1log[5](12x2) Reorder the terms for easier multiplication: 20glox2 + -3 * 5 * 2glo * x = 12 + -1log[5](12x2) Multiply -3 * 5 20glox2 + -15 * 2glo * x = 12 + -1log[5](12x2) Multiply -15 * 2 20glox2 + -30glo * x = 12 + -1log[5](12x2) Multiply glo * x 20glox2 + -30glox = 12 + -1log[5](12x2) Reorder the terms: -30glox + 20glox2 = 12 + -1log[5](12x2) Remove parenthesis around (12x2) -30glox + 20glox2 = 12 + -1glo * 5 * 12x2 Reorder the terms for easier multiplication: -30glox + 20glox2 = 12 + -1 * 5 * 12glo * x2 Multiply -1 * 5 -30glox + 20glox2 = 12 + -5 * 12glo * x2 Multiply -5 * 12 -30glox + 20glox2 = 12 + -60glo * x2 Multiply glo * x2 -30glox + 20glox2 = 12 + -60glox2 Solving -30glox + 20glox2 = 12 + -60glox2 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '60glox2' to each side of the equation. -30glox + 20glox2 + 60glox2 = 12 + -60glox2 + 60glox2 Combine like terms: 20glox2 + 60glox2 = 80glox2 -30glox + 80glox2 = 12 + -60glox2 + 60glox2 Combine like terms: -60glox2 + 60glox2 = 0 -30glox + 80glox2 = 12 + 0 -30glox + 80glox2 = 12 Reorder the terms: -12 + -30glox + 80glox2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -30glox + 80glox2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -15glox + 40glox2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -15glox + 40glox2)' equal to zero and attempt to solve: Simplifying -6 + -15glox + 40glox2 = 0 Solving -6 + -15glox + 40glox2 = 0 Move all terms containing g to the left, all other terms to the right. Add '6' to each side of the equation. -6 + -15glox + 6 + 40glox2 = 0 + 6 Reorder the terms: -6 + 6 + -15glox + 40glox2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -15glox + 40glox2 = 0 + 6 -15glox + 40glox2 = 0 + 6 Combine like terms: 0 + 6 = 6 -15glox + 40glox2 = 6 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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