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Simplifying Log[3](7x + 1) = log[3](4x + 7) Reorder the terms: goL * 3(1 + 7x) = log[3](4x + 7) Reorder the terms for easier multiplication: 3goL(1 + 7x) = log[3](4x + 7) (1 * 3goL + 7x * 3goL) = log[3](4x + 7) (3goL + 21goxL) = log[3](4x + 7) Reorder the terms: 3goL + 21goxL = glo * 3(7 + 4x) Reorder the terms for easier multiplication: 3goL + 21goxL = 3glo(7 + 4x) 3goL + 21goxL = (7 * 3glo + 4x * 3glo) 3goL + 21goxL = (21glo + 12glox) Solving 3goL + 21goxL = 21glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-21glo' to each side of the equation. 3goL + -21glo + 21goxL = 21glo + -21glo + 12glox Reorder the terms: -21glo + 3goL + 21goxL = 21glo + -21glo + 12glox Combine like terms: 21glo + -21glo = 0 -21glo + 3goL + 21goxL = 0 + 12glox -21glo + 3goL + 21goxL = 12glox Add '-12glox' to each side of the equation. -21glo + 3goL + -12glox + 21goxL = 12glox + -12glox Reorder the terms: -21glo + -12glox + 3goL + 21goxL = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -21glo + -12glox + 3goL + 21goxL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(-7l + -4lx + L + 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 '(-7l + -4lx + L + 7xL)' equal to zero and attempt to solve: Simplifying -7l + -4lx + L + 7xL = 0 Reorder the terms: L + -7l + -4lx + 7xL = 0 Solving L + -7l + -4lx + 7xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -7l + -4lx + -1L + 7xL = 0 + -1L Reorder the terms: L + -1L + -7l + -4lx + 7xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -7l + -4lx + 7xL = 0 + -1L -7l + -4lx + 7xL = 0 + -1L Remove the zero: -7l + -4lx + 7xL = -1L Add '7l' to each side of the equation. -7l + -4lx + 7l + 7xL = -1L + 7l Reorder the terms: -7l + 7l + -4lx + 7xL = -1L + 7l Combine like terms: -7l + 7l = 0 0 + -4lx + 7xL = -1L + 7l -4lx + 7xL = -1L + 7l Add '4lx' to each side of the equation. -4lx + 4lx + 7xL = -1L + 7l + 4lx Combine like terms: -4lx + 4lx = 0 0 + 7xL = -1L + 7l + 4lx 7xL = -1L + 7l + 4lx Add '-7xL' to each side of the equation. 7xL + -7xL = -1L + 7l + 4lx + -7xL Combine like terms: 7xL + -7xL = 0 0 = -1L + 7l + 4lx + -7xL Simplifying 0 = -1L + 7l + 4lx + -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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