Logarithm Question....

Determine least integer 'a' such that $3^a 10^5$ given $\log_{10} 3 = 0.4771 $

Question

Logarithm Question.... 

Determine least integer 'a' such that $3^a > 10^5$ given $\log_{10} 3 = 0.4771 $

mathslover · Answer

I did it like this, wanted to make sure, whether the answer is correct or wrong. 

$a \log3 > 5 \log 10$ 

$\implies a \log 3 > 5 $ 

And... $a > \cfrac{5}{0.4771}$

mathslover · Answer

@Miracrown

mathslover · Answer

How will I find the *least integer* now?

hartnn · Answer

yup, its correct...

mathslover · Answer

But, bhaiya, least integer kaise aayega?

hartnn · Answer

whats 5/0.4771
?

mathslover · Answer

10.47 

So, will it be 11?

hartnn · Answer

a>10.47

yes! 11 :)

mathslover · Answer

Oh... I thought, there will be a diff. way to do it.. thank you! :)

anonymous · Answer

Yes it would be 11 as the closest integer to 10.47 is 11

anonymous · Answer

From Where r u doing this questions from , is there any site or from a book

mathslover · Answer

@No.name - book.

mathslover · Answer

I had some questions with me... written on a paper actually. So, these questions are from that pages. (notes)

anonymous · Answer

Okay..