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Simplifying log[5](x + 18) + -1log[5](x + 4) = log[5] * x Reorder the terms: glo * 5(18 + x) + -1log[5](x + 4) = log[5] * x Reorder the terms for easier multiplication: 5glo(18 + x) + -1log[5](x + 4) = log[5] * x (18 * 5glo + x * 5glo) + -1log[5](x + 4) = log[5] * x (90glo + 5glox) + -1log[5](x + 4) = log[5] * x Reorder the terms: 90glo + 5glox + -1glo * 5(4 + x) = log[5] * x Reorder the terms for easier multiplication: 90glo + 5glox + -1 * 5glo(4 + x) = log[5] * x Multiply -1 * 5 90glo + 5glox + -5glo(4 + x) = log[5] * x 90glo + 5glox + (4 * -5glo + x * -5glo) = log[5] * x 90glo + 5glox + (-20glo + -5glox) = log[5] * x Reorder the terms: 90glo + -20glo + 5glox + -5glox = log[5] * x Combine like terms: 90glo + -20glo = 70glo 70glo + 5glox + -5glox = log[5] * x Combine like terms: 5glox + -5glox = 0 70glo + 0 = log[5] * x 70glo = log[5] * x Reorder the terms for easier multiplication: 70glo = 5glo * x Multiply glo * x 70glo = 5glox Solving 70glo = 5glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-5glox' to each side of the equation. 70glo + -5glox = 5glox + -5glox Combine like terms: 5glox + -5glox = 0 70glo + -5glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(14 + -1x) = 0 Ignore the factor 5.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 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 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 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Add 'x' to each side of the equation. -1x + x = -14 + x Combine like terms: -1x + x = 0 0 = -14 + x Simplifying 0 = -14 + x 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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