Number of digits in $12^{300}$

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.

• 12 = 2*2*3, not 2*2*4. – taninamdar Sep 24 '14 at 17:52
• Oh sorry that's a typing mistake.. :) – Harshal Gajjar Sep 24 '14 at 17:52

1 Answer

Hint:

$$\log_{10}12^{300}=300\log_{10}12=300(\log_{10}2+\log_{10}2+\log_{10}3)$$

• My pleasure, glad to help. – vadim123 Sep 25 '14 at 2:29