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Simplifying Log(7)(3x + 10) = log(7)(x + -6) Reorder the terms: goL * 7(10 + 3x) = log(7)(x + -6) Reorder the terms for easier multiplication: 7goL(10 + 3x) = log(7)(x + -6) (10 * 7goL + 3x * 7goL) = log(7)(x + -6) (70goL + 21goxL) = log(7)(x + -6) Reorder the terms: 70goL + 21goxL = glo * 7(-6 + x) Reorder the terms for easier multiplication: 70goL + 21goxL = 7glo(-6 + x) 70goL + 21goxL = (-6 * 7glo + x * 7glo) 70goL + 21goxL = (-42glo + 7glox) Solving 70goL + 21goxL = -42glo + 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '42glo' to each side of the equation. 70goL + 42glo + 21goxL = -42glo + 42glo + 7glox Reorder the terms: 42glo + 70goL + 21goxL = -42glo + 42glo + 7glox Combine like terms: -42glo + 42glo = 0 42glo + 70goL + 21goxL = 0 + 7glox 42glo + 70goL + 21goxL = 7glox Add '-7glox' to each side of the equation. 42glo + 70goL + -7glox + 21goxL = 7glox + -7glox Reorder the terms: 42glo + -7glox + 70goL + 21goxL = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 42glo + -7glox + 70goL + 21goxL = 0 Factor out the Greatest Common Factor (GCF), '7go'. 7go(6l + -1lx + 10L + 3xL) = 0 Ignore the factor 7.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 '(6l + -1lx + 10L + 3xL)' equal to zero and attempt to solve: Simplifying 6l + -1lx + 10L + 3xL = 0 Reorder the terms: 10L + 6l + -1lx + 3xL = 0 Solving 10L + 6l + -1lx + 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 + 6l + -1lx + -10L + 3xL = 0 + -10L Reorder the terms: 10L + -10L + 6l + -1lx + 3xL = 0 + -10L Combine like terms: 10L + -10L = 0 0 + 6l + -1lx + 3xL = 0 + -10L 6l + -1lx + 3xL = 0 + -10L Remove the zero: 6l + -1lx + 3xL = -10L Add '-6l' to each side of the equation. 6l + -1lx + -6l + 3xL = -10L + -6l Reorder the terms: 6l + -6l + -1lx + 3xL = -10L + -6l Combine like terms: 6l + -6l = 0 0 + -1lx + 3xL = -10L + -6l -1lx + 3xL = -10L + -6l Add 'lx' to each side of the equation. -1lx + lx + 3xL = -10L + -6l + lx Combine like terms: -1lx + lx = 0 0 + 3xL = -10L + -6l + lx 3xL = -10L + -6l + lx Add '-3xL' to each side of the equation. 3xL + -3xL = -10L + -6l + lx + -3xL Combine like terms: 3xL + -3xL = 0 0 = -10L + -6l + lx + -3xL Simplifying 0 = -10L + -6l + lx + -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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