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SingaporeAdditional Mathematics

Logarithmic and Exponential Functions

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we solve equations where the unknown is in an exponent or inside a logarithm?

Solve exponential equations by taking logarithms and logarithmic equations by converting to index form, rejecting invalid solutions
A focused answer to the O-Level A-Maths outcome on solving exponential and logarithmic equations. Taking logs to free an exponent, converting logs to index form, and checking validity of solutions.
8 min answer →

What do the graphs of exponential and logarithmic functions look like, and how are they related?

Sketch the graphs of exponential and logarithmic functions, identify their key features, and recognise them as reflections of each other
A focused answer to the O-Level A-Maths outcome on exponential and logarithmic graphs. Their shapes, intercepts, asymptotes, and the inverse relationship that reflects one in the line y equals x.
8 min answer →

How do the laws of logarithms let us combine, split and simplify logarithmic expressions?

State and apply the product, quotient and power laws of logarithms and the change-of-base relationship to simplify and evaluate expressions
A focused answer to the O-Level A-Maths outcome on logarithm laws. The product, quotient and power laws, special values, and the change-of-base formula for evaluating and simplifying logarithms.
8 min answer →

How can we transform a non-linear relationship into a straight line to find its unknown constants?

Transform a non-linear relationship into the form Y equals mX plus c and use the gradient and intercept of the straight-line graph to find unknown constants
A focused answer to the O-Level A-Maths outcome on the linear law. Transforming power and exponential laws into straight-line form, then reading the gradient and intercept to find unknown constants.
9 min answer →