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Simplifying nx + -4[ln(x + -7) + ln(x + 7)] = 0 Reorder the terms: nx + -4[ln(-7 + x) + ln(x + 7)] = 0 nx + -4[(-7 * ln + x * ln) + ln(x + 7)] = 0 nx + -4[(-7ln + lnx) + ln(x + 7)] = 0 Reorder the terms: nx + -4[-7ln + lnx + ln(7 + x)] = 0 nx + -4[-7ln + lnx + (7 * ln + x * ln)] = 0 nx + -4[-7ln + lnx + (7ln + lnx)] = 0 Reorder the terms: nx + -4[-7ln + 7ln + lnx + lnx] = 0 Combine like terms: -7ln + 7ln = 0 nx + -4[0 + lnx + lnx] = 0 nx + -4[lnx + lnx] = 0 Combine like terms: lnx + lnx = 2lnx nx + -4[2lnx] = 0 Remove brackets around [2lnx] nx + -4 * 2lnx = 0 Multiply -4 * 2 nx + -8lnx = 0 Reorder the terms: -8lnx + nx = 0 Solving -8lnx + nx = 0 Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-1nx' to each side of the equation. -8lnx + nx + -1nx = 0 + -1nx Combine like terms: nx + -1nx = 0 -8lnx + 0 = 0 + -1nx -8lnx = 0 + -1nx Remove the zero: -8lnx = -1nx Divide each side by '-8nx'. l = 0.125 Simplifying l = 0.125
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