Logarithmic and Exponential Functions

You will be able to

• Sketch the graph of y = ke^(nx) + a, stating its asymptote y = a, its y-intercept (0, k + a) and its range.
• Sketch the graph of y = k ln(ax + b), stating its domain ax + b > 0, its vertical asymptote x = −b/a and its x-intercept.
• Find the exact coordinates where an exponential or logarithmic graph meets the axes, such as x = ½ ln(4/3).

You will be able to

• Use the laws log ab = log a + log b, log (a/b) = log a − log b and log aⁿ = n log a to combine and simplify logarithms.
• Use the change-of-base rule logₐ b = lg b ÷ lg a to evaluate a logarithm to any base.
• Explain why a slide rule multiplies by adding lengths, because the lengths on a log scale are logarithms.

You will be able to

• Solve an exponential equation by writing both sides as powers of the same base and equating the indices.
• Solve aˣ = b and a^(px + q) = b by taking logarithms, giving the exact answer and its value to 3 significant figures.
• Solve ke^(nx) = b using ln, and apply it to a growth model such as P = 200e^(0.1t).