given log 2=3010, find the number of digits in 3^12×2^8
Hello student,
First of all , we know that between 0 and 1, only 1 digit numbers are present like 3,4,5 etc. And also the LOG of nos. present between 0&1 also comes between 0&1.
Now also there are 2 digit nos. lying between 10 and 100 and, the LOG of these numbers will comes between 1 and 2.
There are 3 digits nos. present between the 100 and 1000 and hence their LOG value lies between 2 and 3.
so now, we have to find the number of digits in 3^12 * 2^8
So the General formula says that if
log n = x.---- , then the number n has x+1 digits to the left of decimal
so now let n = 3^12 * 2^8
take log on both sides
logn = 12 log3+ 8 log2
logn = 5.724+ 2.408 = 8.132
so now by the formula, the number n has 9 digits.
Hope this helps.
