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Simplifying ln(x + 6) + ln(x) = ln(2x + 32) Reorder the terms: ln(6 + x) + ln(x) = ln(2x + 32) (6 * ln + x * ln) + ln(x) = ln(2x + 32) (6ln + lnx) + ln(x) = ln(2x + 32) Multiply ln * x 6ln + lnx + lnx = ln(2x + 32) Combine like terms: lnx + lnx = 2lnx 6ln + 2lnx = ln(2x + 32) Reorder the terms: 6ln + 2lnx = ln(32 + 2x) 6ln + 2lnx = (32 * ln + 2x * ln) 6ln + 2lnx = (32ln + 2lnx) Add '-2lnx' to each side of the equation. 6ln + 2lnx + -2lnx = 32ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln + 0 = 32ln + 2lnx + -2lnx 6ln = 32ln + 2lnx + -2lnx Combine like terms: 2lnx + -2lnx = 0 6ln = 32ln + 0 6ln = 32ln Solving 6ln = 32ln Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-32ln' to each side of the equation. 6ln + -32ln = 32ln + -32ln Combine like terms: 6ln + -32ln = -26ln -26ln = 32ln + -32ln Combine like terms: 32ln + -32ln = 0 -26ln = 0 Divide each side by '-26'. ln = 0 Simplifying ln = 0 The solution to this equation could not be determined.
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