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Simplifying cos(7x + ln(5x)) = 0 Remove parenthesis around (5x) cos(7x + ln * 5x) = 0 Reorder the terms for easier multiplication: cos(7x + 5ln * x) = 0 Multiply ln * x cos(7x + 5lnx) = 0 Reorder the terms: cos(5lnx + 7x) = 0 (5lnx * cos + 7x * cos) = 0 (5clnosx + 7cosx) = 0 Solving 5clnosx + 7cosx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'cosx'. cosx(5ln + 7) = 0Subproblem 1
Set the factor 'cosx' equal to zero and attempt to solve: Simplifying cosx = 0 Solving cosx = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cosx = 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 '(5ln + 7)' equal to zero and attempt to solve: Simplifying 5ln + 7 = 0 Reorder the terms: 7 + 5ln = 0 Solving 7 + 5ln = 0 Move all terms containing c to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5ln = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5ln = 0 + -7 5ln = 0 + -7 Combine like terms: 0 + -7 = -7 5ln = -7 Add '-5ln' to each side of the equation. 5ln + -5ln = -7 + -5ln Combine like terms: 5ln + -5ln = 0 0 = -7 + -5ln Simplifying 0 = -7 + -5ln 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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