AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.12 Logarithmic Function Manipulation
Notes
- Product: $\log_b(mn)=\log_bm+\log_bn$.
- Quotient: $\displaystyle \log_b\frac{m}{n}=\log_bm-\log_bn$.
- Power: $\log_b(m^k)=k\log_bm$.
- Change of base: $\displaystyle \log_ba=\frac{\ln a}{\ln b}$.
Practice
$\log 4+\log 25=$
$\log100=2$.
$\log_3 81^2=$
$2\cdot4=8$.
$\log_2 7$ equals:
Change of base.
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