Chapter 6 - Logarithmic Functions - 6.4 Properties of Logarithms - 6.4 Exercises - Page 517: 65

$ \log _{b} 50000=10$

Given log $_{b} 100=4, \quad \log _{b} 500=6$ $\log _{b} 50000=?$ Using $ \quad \log _{b}(m n)=\log _{b} m+\log _{b} n$ Put $m=100, \quad n=500$ $\quad \therefore \quad \log _{b}(100 \times 500)=\log _{b} 100+\log _{b} 500$ $\Rightarrow \log _{b} 50000=4+6$ $\therefore \log _{b} 50000=10$