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Simplifying Log[5](x + -7) + log[5] * x = log[5] * 30 Reorder the terms: goL * 5(-7 + x) + log[5] * x = log[5] * 30 Reorder the terms for easier multiplication: 5goL(-7 + x) + log[5] * x = log[5] * 30 (-7 * 5goL + x * 5goL) + log[5] * x = log[5] * 30 (-35goL + 5goxL) + log[5] * x = log[5] * 30 Reorder the terms for easier multiplication: -35goL + 5goxL + 5glo * x = log[5] * 30 Multiply glo * x -35goL + 5goxL + 5glox = log[5] * 30 Reorder the terms: 5glox + -35goL + 5goxL = log[5] * 30 Reorder the terms for easier multiplication: 5glox + -35goL + 5goxL = 5 * 30glo Multiply 5 * 30 5glox + -35goL + 5goxL = 150glo Solving 5glox + -35goL + 5goxL = 150glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-150glo' to each side of the equation. 5glox + -35goL + -150glo + 5goxL = 150glo + -150glo Reorder the terms: -150glo + 5glox + -35goL + 5goxL = 150glo + -150glo Combine like terms: 150glo + -150glo = 0 -150glo + 5glox + -35goL + 5goxL = 0 Factor out the Greatest Common Factor (GCF), '5go'. 5go(-30l + lx + -7L + xL) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(-30l + lx + -7L + xL)' equal to zero and attempt to solve: Simplifying -30l + lx + -7L + xL = 0 Reorder the terms: -7L + -30l + lx + xL = 0 Solving -7L + -30l + lx + xL = 0 Move all terms containing g to the left, all other terms to the right. Add '7L' to each side of the equation. -7L + -30l + lx + 7L + xL = 0 + 7L Reorder the terms: -7L + 7L + -30l + lx + xL = 0 + 7L Combine like terms: -7L + 7L = 0 0 + -30l + lx + xL = 0 + 7L -30l + lx + xL = 0 + 7L Remove the zero: -30l + lx + xL = 7L Add '30l' to each side of the equation. -30l + lx + 30l + xL = 7L + 30l Reorder the terms: -30l + 30l + lx + xL = 7L + 30l Combine like terms: -30l + 30l = 0 0 + lx + xL = 7L + 30l lx + xL = 7L + 30l Add '-1lx' to each side of the equation. lx + -1lx + xL = 7L + 30l + -1lx Combine like terms: lx + -1lx = 0 0 + xL = 7L + 30l + -1lx xL = 7L + 30l + -1lx Add '-1xL' to each side of the equation. xL + -1xL = 7L + 30l + -1lx + -1xL Combine like terms: xL + -1xL = 0 0 = 7L + 30l + -1lx + -1xL Simplifying 0 = 7L + 30l + -1lx + -1xL 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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