↧↧↧ Detailed Video Solution to the Problem ↧↧↧



We need to find the values of x for which the units digit of 2*\(3^x\) = 4

When we multiply some number with 2 then we can get units digit of 4 only when we have the units digit of the number as 2 or 7
As 2*2 = 4 and 2*7 = 14 making the units' digit as 4 in both the cases

=> Units digit of \(3^x\) = 2 or 7
Since 3 is an odd number of units' digit of any power of 3 cannot be 2

=> Units digit of \(3^x\) = 7

Now lets start by finding the cyclicity of units' digit in powers of 3

\(3^1\) units’ digit is 3
\(3^2\) units’ digit is 9
\(3^3\) units’ digit is 7
\(3^4\) units’ digit is 1
\(3^5\) units’ digit is 3

That means that units digit of power of 3 has a cycle of 4

=> In order to get a units digit of 7, we need to divided the power of 3 by 4 to get a remainder of 3

A. 12 , 12 when divided by 4 gives 0 remainder => NOT POSSIBLE
B. 13 , 12 when divided by 4 gives 1 remainder => NOT POSSIBLE
C. 14 , 12 when divided by 4 gives 2 remainder => NOT POSSIBLE
D. 15 , 12 when divided by 4 gives 3 remainder => POSSIBLE
E. 16 , 12 when divided by 4 gives 0 remainder => NOT POSSIBLE

So, Answer will be D
Hope it helps!­

Link to Theory for Last Two digits of exponents here.

Link to Theory for Units' digit of exponents here.