Exponential and logarithmic functions

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of coronavirus, radioactive decay and compound interest. Logarithmic functions, the inverse of exponential functions, are essential for solving equations involving exponential terms and are applied in measuring sound intensity, earthquake magnitude, and data compression.

These two functions help analyse processes that change rapidly or span vast scales. Understanding exponential functions requires knowledge of Index Laws, solving exponential equations and sketching graphs of exponential functions. Similarly, understanding logarithmic functions requires knowledge of laws of logarithms, solving logarithmic equations and sketching graphs of logarithmic functions.

This resource revises exponential and logarithmic functions and within this topic there are 2 key concepts:

• Solving exponential and logarithmic equations
• Graphing of exponential and logarithmic functions

To determine if this resource will benefit you, start by answering the following questions.

• What are key features of exponential and logarithmic functions, and how are they related?
• How are the laws of indices and logarithms used to solve logarithmic and exponential equations?
• How do changes to the base of a logarithmic or exponential function impact its graph and growth rate?

The answers to these questions are provided on the following pages. Use this resource to refresh your memory, reinforce your understanding of these concepts, and prepare more effectively for university-level learning.

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