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	Prior knowledge	Used for
Financial Mathematics B	- future value formula	- applications of logarithms to compound interest
Indices A	- index laws	- logarithm laws
Indices B	- negative indices	- logarithm laws
Indices C	- fractional indices	- logarithm laws
Equations C	- solving complex equations	- solving logarithmic equations
Non-Linear Relationships C	- graphs of exponential functions	- graphs of logarithmic functions

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