Logarithmic and exponential functions

You will be able to

• Describe the graph of y = e^(kx) + c for k > 0 and k < 0, and state the domain and range of f and of its inverse, a ln function reflected in y = x.
• Determine the exact solution and its 3 s.f. value for a × b^(px + q) = r and for 3^(x + 1) = 4^(2x − 1), by taking ln of both sides.
• Explain why an inequality reverses when it is divided by a negative number such as ln(½), and why the indices of different bases cannot simply be equated.

You will be able to

• Deduce from a table of values whether y = kx^n or y = k a^x fits, and state its straight-line form with ln y against ln x or against x.
• Calculate the gradient and intercept from two points far apart on the line, and determine k and n (or k and a) to 3 s.f.
• Explain why the wrong transformation leaves a curve, and why two points close together make the gradient unreliable.