#NumberAndAlgebra #Path #Adv >[!info]- [Logarithms (Path) | NSW curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-k-10-2022/content/stage-5/fa0379c0d0) >- 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 $x=\log_ay$ where $a>0$ and $a≠1$ - 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 $x=\log_ay$ - Generalise that $x=\log_ay$ 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