Logarithms

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Logarithms (Path) | NSW curriculum Website

• MA5-LOG-P-01 establishes and applies the laws of logarithms to solve problems

📖 Prior Knowledge

Content	Prerequisite relationships
Financial Mathematics B	- Apply the compound interest formula → Solve exponential and logarithmic equations
Indices A	- Apply index laws to algebraic terms → Define a logarithm
Non-linear Relationships B	- Graph exponentials and identify their features → Compare exponential and logarithmic graphs
Indices B	- Convert between negative and positive indices → Translate between index and logarithmic form
Indices C	- Describe and use fractional indices → Translate between index and logarithmic form
Non-Linear Relationships C	- Graph exponentials and describe transformations → Compare exponential and logarithmic graphs

Examine logarithms both numerically and graphically.pdf

• 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 $x={\log }_{a}y$
• Generalise that $x={\log }_{a}y$ is an increasing function when $a>1$ and decreasing when $0<a<1$

Establish and apply the laws of logarithms to solve problems.pdf

• 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