Logarithms

𝐡𝑃=𝐴log𝐡𝐴=𝑃
23=8log28=3
210=1024log2100=2
210=1024log21024=10
ln=log𝑒(natural log)

Logarithm Properties

logπ‘Žπ‘Ž=1logπ‘Ž1=0logπ‘Žπ‘Žπ‘₯=π‘₯π‘Žlogπ‘Žπ‘₯=π‘₯

Tip

You can view logπ‘Žπ‘Žπ‘₯=π‘₯ as logπ‘Ž and π‘Ž cancelling each other.

Exponential Functions

Related

Let𝑦=π‘Žπ‘₯,thusπ‘₯=logπ‘Žπ‘¦

The same properties from exponential functions (e.g. π‘Ž>0) also apply to logarithms. π‘Ž can also not equal to 1. See 7.01 + 7.02 - Exponential Functions and Euler’s Number for every property.