Question

If log3n+log9nlog3n+log9n is whole number, then how many numbers possible for n between 100 to 100?

Answer 1

The option for this question are misssing: following are the options:

A)1

B)20

C)111

D) 150

Solution

The answer for this is option A

We can write logN base3=(logN baseX/log3 baseX);

And logN base9=(logN baseX/log9 baseX);

Now, logN base3+logN base9= ( logN baseX / log3 baseX + logN baseX / log9 baseX)

=logN baseX (1/log3 baseX + 1/2log3 baseX) bcz (3 square =9)

=logN baseX ( 3log3 baseX / 2log3 baseX *log3 baseX) by simple addition

=logN base X ( 3/2log3 base X)

or =logN base X *3 / log9 base X

or =3 * logN base 9:

So N should be 81 because it is a 9 square and it also between 10 to 100.