Logarithms
\(2^x=16\ \rightarrow\ \log_216=x\)
"2 to some x is 16." "What power do I need to raise 2 to, to get 16? x."
Generally, what power do I have to raise the base to get the result?
Logarithm properties
- Product rule: \(\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)\)
- Quotient rule: \(\log_b\left(\frac{M}{N}\right)=\log_b\left(M\right)-\log_b\left(N\right)\)
- Power rule: \(\log_b\left(M^p\right)=p\log_b\left(M\right)\)
- Change of base rule: \(\log_bA=\dfrac{\log_cA}{\log_cB}\)
Domain of the logarithm: \(x>0\)