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Simplifying Lg(5 + -3x) = lg(x + -3) (5 * gL + -3x * gL) = lg(x + -3) (5gL + -3gxL) = lg(x + -3) Reorder the terms: 5gL + -3gxL = gl(-3 + x) 5gL + -3gxL = (-3 * gl + x * gl) 5gL + -3gxL = (-3gl + glx) Solving 5gL + -3gxL = -3gl + glx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3gl' to each side of the equation. 5gL + 3gl + -3gxL = -3gl + 3gl + glx Combine like terms: -3gl + 3gl = 0 5gL + 3gl + -3gxL = 0 + glx 5gL + 3gl + -3gxL = glx Add '-1glx' to each side of the equation. 5gL + 3gl + -1glx + -3gxL = glx + -1glx Combine like terms: glx + -1glx = 0 5gL + 3gl + -1glx + -3gxL = 0 Factor out the Greatest Common Factor (GCF), 'g'. g(5L + 3l + -1lx + -3xL) = 0Subproblem 1
Set the factor 'g' equal to zero and attempt to solve: Simplifying g = 0 Solving g = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g = 0Subproblem 2
Set the factor '(5L + 3l + -1lx + -3xL)' equal to zero and attempt to solve: Simplifying 5L + 3l + -1lx + -3xL = 0 Solving 5L + 3l + -1lx + -3xL = 0 Move all terms containing g to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + 3l + -1lx + -5L + -3xL = 0 + -5L Reorder the terms: 5L + -5L + 3l + -1lx + -3xL = 0 + -5L Combine like terms: 5L + -5L = 0 0 + 3l + -1lx + -3xL = 0 + -5L 3l + -1lx + -3xL = 0 + -5L Remove the zero: 3l + -1lx + -3xL = -5L Add '-3l' to each side of the equation. 3l + -1lx + -3l + -3xL = -5L + -3l Reorder the terms: 3l + -3l + -1lx + -3xL = -5L + -3l Combine like terms: 3l + -3l = 0 0 + -1lx + -3xL = -5L + -3l -1lx + -3xL = -5L + -3l Add 'lx' to each side of the equation. -1lx + lx + -3xL = -5L + -3l + lx Combine like terms: -1lx + lx = 0 0 + -3xL = -5L + -3l + lx -3xL = -5L + -3l + lx Add '3xL' to each side of the equation. -3xL + 3xL = -5L + -3l + lx + 3xL Combine like terms: -3xL + 3xL = 0 0 = -5L + -3l + lx + 3xL Simplifying 0 = -5L + -3l + lx + 3xL The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
g = {0}
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