Question

If $lo{g}_{10}3=0.4771$, then find the number of zeroes after the decimal in $3^{-100}$

Answer 1

Let $t=3^{-100}$
Taking logarithm, we get
${\log }_{10}t=-100{\log }_{10}3=-100\times 0.4771=-47.71$
$\Rightarrow t={10}^{-47.71}$
$\therefore$ Number of zeroes in $3^{-100}$ after decimal are $47$.