7/21/2023 0 Comments Lambda calculus cheat sheet![]() ![]() For example, to solve 2^x = 16, take the logarithm base 2 of both sides to get x = 4. Solving Exponential Equations: To solve an exponential equation, take the logarithm of both sides of the equation.Solve for x to get x = 2, then substitute x = 2 into either equation to get y = 2.Īn exponential equation is an equation with a variable in the exponent. ![]() For example, to solve the system 3x + 2y = 10 and 2x - 4y = -4, multiply the first equation by 2 to get 6x + 4y = 20, then add the second equation to eliminate y and get 8x = 16. Elimination Method: To solve a system of equations using the elimination method, add or subtract the equations to eliminate one of the variables, then solve for the remaining variable.Solve for x to get x = 2, then substitute x = 2 into either equation to get y = 5. For example, to solve the system x + y = 7 and 2x - y = 1, solve the first equation for y to get y = 7 - x, then substitute 7 - x for y in the second equation to get 2x - (7 - x) = 1. Substitution Method: To solve a system of equations using the substitution method, solve one of the equations for one of the variables, then substitute the expression for that variable into the other equation.For example, to solve x^2 + 6x + 5 = 0, add and subtract (6/2)^2 = 9 to get (x + 3)^2 - 4 = 0, then factor to get (x + 3 - 2)(x + 3 + 2) = 0, which gives x = -5 or x = -1.Ī system of equations is a set of equations with multiple variables. To complete the square, add and subtract (b/2a)^2 to the equation, then factor the resulting trinomial. Completing the Square: Completing the square is a method for solving quadratic equations. ![]()
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