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Simplifying lg(x + 3) + -4lg(x + 3) + 3 = 0 Reorder the terms: gl(3 + x) + -4lg(x + 3) + 3 = 0 (3 * gl + x * gl) + -4lg(x + 3) + 3 = 0 (3gl + glx) + -4lg(x + 3) + 3 = 0 Reorder the terms: 3gl + glx + -4gl(3 + x) + 3 = 0 3gl + glx + (3 * -4gl + x * -4gl) + 3 = 0 3gl + glx + (-12gl + -4glx) + 3 = 0 Reorder the terms: 3 + 3gl + -12gl + glx + -4glx = 0 Combine like terms: 3gl + -12gl = -9gl 3 + -9gl + glx + -4glx = 0 Combine like terms: glx + -4glx = -3glx 3 + -9gl + -3glx = 0 Solving 3 + -9gl + -3glx = 0 Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -9gl + -3 + -3glx = 0 + -3 Reorder the terms: 3 + -3 + -9gl + -3glx = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -9gl + -3glx = 0 + -3 -9gl + -3glx = 0 + -3 Combine like terms: 0 + -3 = -3 -9gl + -3glx = -3 Reorder the terms: 3 + -9gl + -3glx = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -9gl + -3glx = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -3gl + -1glx) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -3gl + -1glx)' equal to zero and attempt to solve: Simplifying 1 + -3gl + -1glx = 0 Solving 1 + -3gl + -1glx = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -3gl + -1 + -1glx = 0 + -1 Reorder the terms: 1 + -1 + -3gl + -1glx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3gl + -1glx = 0 + -1 -3gl + -1glx = 0 + -1 Combine like terms: 0 + -1 = -1 -3gl + -1glx = -1 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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