Topic 14 0.0 / 5 ? MathematicsLogarithms and exponentialsASEdexcel Created by: Jemma1494Created on: 06-06-21 18:38 Exponentials In the form f(x) = a^x Exponential graphs have increasing gradients and asymptotes 1 of 8 y =e^x e = 2.71828 If f(x) = e^x then f’(x) = e^x If f(x) = e^kx then f’(x) = ke^kx 2 of 8 Logarithms Written as loga n = x Equivalent to a^x = n So 3^2 = 9 Is also log3 9 = 2 3 of 8 Natural log Has a base of e 4 of 8 Log rules loga 1 = 0 loga a = 1 loga x + loga y = loga xy loga x - loga y = loga x/y loga (x^k) = kloga x loga (1/x) = loga (x^-1) = -loga x 5 of 8 Solving equations using logs A^x = B (Take logs of both side) x = loga B 6 of 8 y = e^x and y = lnx Reflections of each other in the line y = x 7 of 8 Converting exponential to linear y = ax^n log y = log ax^n log y = log a + nlog x y = c + mx 8 of 8
Comments
No comments have yet been made