M - Pure 1 - 14) Exponentials and logarithms

Question 1

How differentiation works with e

Answer 1

• If f(x) = e^x, f’(x) = e^x
• If f(x) = e^kx, f’(x) = ke^kx

Question 2

List of all laws of logarithms

Answer 2

• log_ax + log_ay = log_axy
• log_ax - log_ay = log_ax/y
• log_a(x^k) = k log_ax
• log_a(1/x) = log_a(x^-1) = -log_ax
• log_aa = 1
• log_a1 = 0

Question 3

Graph of y = ln x

Answer 3

Reflection of the graph of y = e^x in the line y = x

Question 4

Equivalent values of e^{ln x}

Answer 4

e^{ln x} = ln (e^x) = x

Question 5

Graph of y = axⁿ

Answer 5

Axis of log x and log y. Straight line with a gradient of n and vertical intercept of log a

Question 6

Graph of y = ab^x

Answer 6

Axis of x and log y. Straight line with a gradient of log b and vertical intercept of log a