How to calculate the number of digits in Large Exponents

Dear Aspirants

Today we bring you a very important trick to calculate the number of digits in a number of a very large exponent.

Suppose you are asked to take out the number of digits in A^B.  The number of digits in the given number is equal to the value calculate by the following formula:

Number of digits in A^B is 

Example: Find the number of digits in 72¹²⁰.

Solution: The value of (Log 72¹²⁰) = ( 120 X log 72)

              Calculating the value of log72 : log 72 = log (2³X3²)  

                                                log 72 = (3log2 + 2log3)               

                                                As log2= 0.301 and log3= 0.4771, putting the value in the above equation, we get

                                                log 72= 1.86 (approx.)

                                                Therefore,(120 x 1.86 = 223)

Hence, the number of digits in 72¹²⁰ = (1+223) = 224

Thanks!