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Simplifying Log[3](7x + -6) = log[3](4x + 9) Reorder the terms: goL * 3(-6 + 7x) = log[3](4x + 9) Reorder the terms for easier multiplication: 3goL(-6 + 7x) = log[3](4x + 9) (-6 * 3goL + 7x * 3goL) = log[3](4x + 9) (-18goL + 21goxL) = log[3](4x + 9) Reorder the terms: -18goL + 21goxL = glo * 3(9 + 4x) Reorder the terms for easier multiplication: -18goL + 21goxL = 3glo(9 + 4x) -18goL + 21goxL = (9 * 3glo + 4x * 3glo) -18goL + 21goxL = (27glo + 12glox) Solving -18goL + 21goxL = 27glo + 12glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-27glo' to each side of the equation. -18goL + -27glo + 21goxL = 27glo + -27glo + 12glox Reorder the terms: -27glo + -18goL + 21goxL = 27glo + -27glo + 12glox Combine like terms: 27glo + -27glo = 0 -27glo + -18goL + 21goxL = 0 + 12glox -27glo + -18goL + 21goxL = 12glox Add '-12glox' to each side of the equation. -27glo + -18goL + -12glox + 21goxL = 12glox + -12glox Reorder the terms: -27glo + -12glox + -18goL + 21goxL = 12glox + -12glox Combine like terms: 12glox + -12glox = 0 -27glo + -12glox + -18goL + 21goxL = 0 Factor out the Greatest Common Factor (GCF), '3go'. 3go(-9l + -4lx + -6L + 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 '(-9l + -4lx + -6L + 7xL)' equal to zero and attempt to solve: Simplifying -9l + -4lx + -6L + 7xL = 0 Reorder the terms: -6L + -9l + -4lx + 7xL = 0 Solving -6L + -9l + -4lx + 7xL = 0 Move all terms containing g to the left, all other terms to the right. Add '6L' to each side of the equation. -6L + -9l + -4lx + 6L + 7xL = 0 + 6L Reorder the terms: -6L + 6L + -9l + -4lx + 7xL = 0 + 6L Combine like terms: -6L + 6L = 0 0 + -9l + -4lx + 7xL = 0 + 6L -9l + -4lx + 7xL = 0 + 6L Remove the zero: -9l + -4lx + 7xL = 6L Add '9l' to each side of the equation. -9l + -4lx + 9l + 7xL = 6L + 9l Reorder the terms: -9l + 9l + -4lx + 7xL = 6L + 9l Combine like terms: -9l + 9l = 0 0 + -4lx + 7xL = 6L + 9l -4lx + 7xL = 6L + 9l Add '4lx' to each side of the equation. -4lx + 4lx + 7xL = 6L + 9l + 4lx Combine like terms: -4lx + 4lx = 0 0 + 7xL = 6L + 9l + 4lx 7xL = 6L + 9l + 4lx Add '-7xL' to each side of the equation. 7xL + -7xL = 6L + 9l + 4lx + -7xL Combine like terms: 7xL + -7xL = 0 0 = 6L + 9l + 4lx + -7xL Simplifying 0 = 6L + 9l + 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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