ABC26GN2099 · Logarithms

$\log \left(4^{9} \times 5^{17}\right)=\log \left(4^{9}\right)+\log \left(5^{17}\right)=\log \left(2^{2}\right)^{9}+\log \left(5^{17}\right)$ $=\log \left(2^{18}\right)+\log \left(5^{17}\right)$ $=18 \log 2+17 \log 5=18 \log 2+17(\log 10-\log 2)$ $=18 \log 2+17 \log 10-17 \log 2=\log 2+17 \log 10$ $=0.3010+17 \times 1=17.3010$. $\therefore \quad$ Characteristic $=17$. Hence, the number of digits in $\left(4^{9} \times 5^{17}\right)=18$.