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Simplifying Log(10x + -4x) = log(10 + -3x) Combine like terms: 10x + -4x = 6x goL(6x) = log(10 + -3x) Remove parenthesis around (6x) goL * 6x = log(10 + -3x) Reorder the terms for easier multiplication: 6goL * x = log(10 + -3x) Multiply goL * x 6goxL = log(10 + -3x) 6goxL = (10 * glo + -3x * glo) 6goxL = (10glo + -3glox) Solving 6goxL = 10glo + -3glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-10glo' to each side of the equation. -10glo + 6goxL = 10glo + -10glo + -3glox Combine like terms: 10glo + -10glo = 0 -10glo + 6goxL = 0 + -3glox -10glo + 6goxL = -3glox Add '3glox' to each side of the equation. -10glo + 3glox + 6goxL = -3glox + 3glox Combine like terms: -3glox + 3glox = 0 -10glo + 3glox + 6goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-10l + 3lx + 6xL) = 0Subproblem 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 '(-10l + 3lx + 6xL)' equal to zero and attempt to solve: Simplifying -10l + 3lx + 6xL = 0 Solving -10l + 3lx + 6xL = 0 Move all terms containing g to the left, all other terms to the right. Add '10l' to each side of the equation. -10l + 3lx + 10l + 6xL = 0 + 10l Reorder the terms: -10l + 10l + 3lx + 6xL = 0 + 10l Combine like terms: -10l + 10l = 0 0 + 3lx + 6xL = 0 + 10l 3lx + 6xL = 0 + 10l Remove the zero: 3lx + 6xL = 10l Add '-3lx' to each side of the equation. 3lx + -3lx + 6xL = 10l + -3lx Combine like terms: 3lx + -3lx = 0 0 + 6xL = 10l + -3lx 6xL = 10l + -3lx Add '-6xL' to each side of the equation. 6xL + -6xL = 10l + -3lx + -6xL Combine like terms: 6xL + -6xL = 0 0 = 10l + -3lx + -6xL Simplifying 0 = 10l + -3lx + -6xL 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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