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Simplifying 7Log(3x) + 3log(5x) = 15log(10) Remove parenthesis around (3x) 7goL * 3x + 3log(5x) = 15log(10) Reorder the terms for easier multiplication: 7 * 3goL * x + 3log(5x) = 15log(10) Multiply 7 * 3 21goL * x + 3log(5x) = 15log(10) Multiply goL * x 21goxL + 3log(5x) = 15log(10) Remove parenthesis around (5x) 21goxL + 3glo * 5x = 15log(10) Reorder the terms for easier multiplication: 21goxL + 3 * 5glo * x = 15log(10) Multiply 3 * 5 21goxL + 15glo * x = 15log(10) Multiply glo * x 21goxL + 15glox = 15log(10) Reorder the terms: 15glox + 21goxL = 15log(10) Reorder the terms for easier multiplication: 15glox + 21goxL = 15 * 10glo Multiply 15 * 10 15glox + 21goxL = 150glo Solving 15glox + 21goxL = 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. 15glox + -150glo + 21goxL = 150glo + -150glo Reorder the terms: -150glo + 15glox + 21goxL = 150glo + -150glo Combine like terms: 150glo + -150glo = 0 -150glo + 15glox + 21goxL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(-50l + 5lx + 7xL) = 0 Ignore the factor 3.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 '(-50l + 5lx + 7xL)' equal to zero and attempt to solve: Simplifying -50l + 5lx + 7xL = 0 Solving -50l + 5lx + 7xL = 0 Move all terms containing g to the left, all other terms to the right. Add '50l' to each side of the equation. -50l + 5lx + 50l + 7xL = 0 + 50l Reorder the terms: -50l + 50l + 5lx + 7xL = 0 + 50l Combine like terms: -50l + 50l = 0 0 + 5lx + 7xL = 0 + 50l 5lx + 7xL = 0 + 50l Remove the zero: 5lx + 7xL = 50l Add '-5lx' to each side of the equation. 5lx + -5lx + 7xL = 50l + -5lx Combine like terms: 5lx + -5lx = 0 0 + 7xL = 50l + -5lx 7xL = 50l + -5lx Add '-7xL' to each side of the equation. 7xL + -7xL = 50l + -5lx + -7xL Combine like terms: 7xL + -7xL = 0 0 = 50l + -5lx + -7xL Simplifying 0 = 50l + -5lx + -7xL 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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