Given: $\log_{10}2= 0.3010$ and $\log_{10}3=0.4771 $, find the numer of digits in $12^{300}$
Options: $324,323,325,\text{Other}$
Actually I tried breaking 12 into 2*2*4.. And then tried to guess the series in no of digits increasing per multiplication of a term.. This really doesn't help.. I am not able to find the use of Log in the question.. :/ Thanks in advance.
Hint:
$$\log_{10}12^{300}=300\log_{10}12=300(\log_{10}2+\log_{10}2+\log_{10}3)$$