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Simplifying log[9](5 + -2k) = log[9](-4k + -7) Reorder the terms for easier multiplication: 9glo(5 + -2k) = log[9](-4k + -7) (5 * 9glo + -2k * 9glo) = log[9](-4k + -7) Reorder the terms: (-18gklo + 45glo) = log[9](-4k + -7) (-18gklo + 45glo) = log[9](-4k + -7) Reorder the terms: -18gklo + 45glo = glo * 9(-7 + -4k) Reorder the terms for easier multiplication: -18gklo + 45glo = 9glo(-7 + -4k) -18gklo + 45glo = (-7 * 9glo + -4k * 9glo) Reorder the terms: -18gklo + 45glo = (-36gklo + -63glo) -18gklo + 45glo = (-36gklo + -63glo) Solving -18gklo + 45glo = -36gklo + -63glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '36gklo' to each side of the equation. -18gklo + 36gklo + 45glo = -36gklo + 36gklo + -63glo Combine like terms: -18gklo + 36gklo = 18gklo 18gklo + 45glo = -36gklo + 36gklo + -63glo Combine like terms: -36gklo + 36gklo = 0 18gklo + 45glo = 0 + -63glo 18gklo + 45glo = -63glo Add '63glo' to each side of the equation. 18gklo + 45glo + 63glo = -63glo + 63glo Combine like terms: 45glo + 63glo = 108glo 18gklo + 108glo = -63glo + 63glo Combine like terms: -63glo + 63glo = 0 18gklo + 108glo = 0 Factor out the Greatest Common Factor (GCF), '18glo'. 18glo(k + 6) = 0 Ignore the factor 18.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 '(k + 6)' equal to zero and attempt to solve: Simplifying k + 6 = 0 Reorder the terms: 6 + k = 0 Solving 6 + k = 0 Move all terms containing g to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + k = 0 + -6 Combine like terms: 6 + -6 = 0 0 + k = 0 + -6 k = 0 + -6 Combine like terms: 0 + -6 = -6 k = -6 Add '-1k' to each side of the equation. k + -1k = -6 + -1k Combine like terms: k + -1k = 0 0 = -6 + -1k Simplifying 0 = -6 + -1k 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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