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Simplifying log7(-1x + -6) = log7(x + 8) Reorder the terms: g7lo(-6 + -1x) = log7(x + 8) (-6 * g7lo + -1x * g7lo) = log7(x + 8) (-6g7lo + -1g7lox) = log7(x + 8) Reorder the terms: -6g7lo + -1g7lox = g7lo(8 + x) -6g7lo + -1g7lox = (8 * g7lo + x * g7lo) -6g7lo + -1g7lox = (8g7lo + g7lox) Solving -6g7lo + -1g7lox = 8g7lo + g7lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-8g7lo' to each side of the equation. -6g7lo + -8g7lo + -1g7lox = 8g7lo + -8g7lo + g7lox Combine like terms: -6g7lo + -8g7lo = -14g7lo -14g7lo + -1g7lox = 8g7lo + -8g7lo + g7lox Combine like terms: 8g7lo + -8g7lo = 0 -14g7lo + -1g7lox = 0 + g7lox -14g7lo + -1g7lox = g7lox Add '-1g7lox' to each side of the equation. -14g7lo + -1g7lox + -1g7lox = g7lox + -1g7lox Combine like terms: -1g7lox + -1g7lox = -2g7lox -14g7lo + -2g7lox = g7lox + -1g7lox Combine like terms: g7lox + -1g7lox = 0 -14g7lo + -2g7lox = 0 Factor out the Greatest Common Factor (GCF), '-2g7lo'. -2g7lo(7 + x) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'g7lo' equal to zero and attempt to solve: Simplifying g7lo = 0 Solving g7lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g7lo = 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 '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Add '-1x' to each side of the equation. x + -1x = -7 + -1x Combine like terms: x + -1x = 0 0 = -7 + -1x Simplifying 0 = -7 + -1x 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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