Logarithms - intermediate

This lesson comprises three (3) master classes focusing on:

• Defining logarithms
• Laws of logarithms
• Graphing exponents and logarithms
• Logarithmic scales

Content:

MA5-LOG-P-01

Examine logarithms both numerically and graphically

• Define the term logarithm: the logarithm of a number to any positive base \( a \) is the index to which \( a \) is raised to give this number
• Recognise equivalence where \( y=a^x \) is equivalent to \( x= \log_a y \) where \( a>0 \) and \( a \ne 1 \)
• Translate statements expressing a number in index form into equivalent statements expressing the logarithm of the number
• Use graphing applications to compare and contrast graphs for the functions \( y=a^x \) and \( y= \log_a x \) 
• Generalise that \( y= \log_a x \) is an increasing function when  \( a \ge 1 \) and decreasing when  \( 0<a<1 \)

Establish and apply the laws of logarithms to solve problems

• Deduce laws of logarithms from laws of indices
• Establish and use a variety of logarithmic results
• Apply the laws of logarithms to evaluate and simplify expressions
• Solve simple equations that involve exponents or logarithms
• Examine logarithmic scales and explain their use in various contexts