Logarithmic and exponential functions

Understanding Exponential and Logarithmic Functions

Become proficient with the concept of exponential functions, understanding its base, exponent, and how changing each affects the function’s behaviour.
Identify and utilise the properties of exponential functions to simplify expressions and to solve equations.
Plot and interpret the graphs of exponential functions. Recognise the exponential growth and decay.

Comprehend the principles of logarithmic functions, focusing on the relationship between a logarithm, its base, and the number.
Apply the three main properties of logarithms, which include product, quotient, and power, to simplify logarithmic expressions.
Exploit the inverse relationship between exponential and logarithmic functions to transform equations.
Plot and interpret the graphs of logarithmic functions. Notice the behaviour of the graphs and the asymptotes.

Learn to solve exponential equations, both graphically and algebraically.
Develop skills to solve logarithmic equations, using techniques such as making the bases identical, changing the base, or using the one-to-one property of logarithm.
Understand the process to solve equations involving both exponential and logarithmic functions.

Apply your knowledge of exponential and logarithmic functions to solve real-world problems, such as those involving population growth, radioactive decay, and compounding interest.
Comprehend the concept of continuous compounding and its link with the natural logarithm, e.
Utilise the concept of the half-life of a substance in modelling its decay.