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Simplifying Log[3](7x + 3) + -1log[3](10x + 5) = 3 Reorder the terms: goL * 3(3 + 7x) + -1log[3](10x + 5) = 3 Reorder the terms for easier multiplication: 3goL(3 + 7x) + -1log[3](10x + 5) = 3 (3 * 3goL + 7x * 3goL) + -1log[3](10x + 5) = 3 (9goL + 21goxL) + -1log[3](10x + 5) = 3 Reorder the terms: 9goL + 21goxL + -1glo * 3(5 + 10x) = 3 Reorder the terms for easier multiplication: 9goL + 21goxL + -1 * 3glo(5 + 10x) = 3 Multiply -1 * 3 9goL + 21goxL + -3glo(5 + 10x) = 3 9goL + 21goxL + (5 * -3glo + 10x * -3glo) = 3 9goL + 21goxL + (-15glo + -30glox) = 3 Reorder the terms: -15glo + -30glox + 9goL + 21goxL = 3 Solving -15glo + -30glox + 9goL + 21goxL = 3 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Reorder the terms: -3 + -15glo + -30glox + 9goL + 21goxL = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -15glo + -30glox + 9goL + 21goxL = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -5glo + -10glox + 3goL + 7goxL) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -5glo + -10glox + 3goL + 7goxL)' equal to zero and attempt to solve: Simplifying -1 + -5glo + -10glox + 3goL + 7goxL = 0 Solving -1 + -5glo + -10glox + 3goL + 7goxL = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -5glo + -10glox + 3goL + 1 + 7goxL = 0 + 1 Reorder the terms: -1 + 1 + -5glo + -10glox + 3goL + 7goxL = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5glo + -10glox + 3goL + 7goxL = 0 + 1 -5glo + -10glox + 3goL + 7goxL = 0 + 1 Combine like terms: 0 + 1 = 1 -5glo + -10glox + 3goL + 7goxL = 1 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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