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