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Simplifying Log(32x + 1) = log(7x) Reorder the terms: goL(1 + 32x) = log(7x) (1 * goL + 32x * goL) = log(7x) (1goL + 32goxL) = log(7x) Remove parenthesis around (7x) 1goL + 32goxL = glo * 7x Reorder the terms for easier multiplication: 1goL + 32goxL = 7glo * x Multiply glo * x 1goL + 32goxL = 7glox Solving 1goL + 32goxL = 7glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-7glox' to each side of the equation. 1goL + -7glox + 32goxL = 7glox + -7glox Reorder the terms: -7glox + 1goL + 32goxL = 7glox + -7glox Combine like terms: 7glox + -7glox = 0 -7glox + 1goL + 32goxL = 0 Factor out the Greatest Common Factor (GCF), 'go'. go(-7lx + L + 32xL) = 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 '(-7lx + L + 32xL)' equal to zero and attempt to solve: Simplifying -7lx + L + 32xL = 0 Reorder the terms: L + -7lx + 32xL = 0 Solving L + -7lx + 32xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-1L' to each side of the equation. L + -7lx + -1L + 32xL = 0 + -1L Reorder the terms: L + -1L + -7lx + 32xL = 0 + -1L Combine like terms: L + -1L = 0 0 + -7lx + 32xL = 0 + -1L -7lx + 32xL = 0 + -1L Remove the zero: -7lx + 32xL = -1L Add '7lx' to each side of the equation. -7lx + 7lx + 32xL = -1L + 7lx Combine like terms: -7lx + 7lx = 0 0 + 32xL = -1L + 7lx 32xL = -1L + 7lx Add '-32xL' to each side of the equation. 32xL + -32xL = -1L + 7lx + -32xL Combine like terms: 32xL + -32xL = 0 0 = -1L + 7lx + -32xL Simplifying 0 = -1L + 7lx + -32xL 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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