What will be the value of (99/100) raise to the power 100

Question

               100

(99/100)

Answer 1

It's about 0.366.

Answer 2

If you are asked to do this without calculator, You can use log with with base 10 to solve it.

In this case, for log_10(x) I will use log(x)

 

(99/100)^100

= log((99/100)^100)

= 100*log(99/100)                    because according to logarithm laws, log_b(x^n)=n*log_b(x)

= 100*(log(99)-log(100))         because according to logarithm laws, log(a/b)=log(a)-log(b)

 

Since log(100)=2 because 10^2 = 100 and log(99) is approximately 1.99(there is a way to find logs for this type without calculator. Let me know if you need that much detail for your work)

 

=100*(1.99-2)

=-0.43648               (Now undo the log with base 10 by making this number the power of 10)

=10^-0.43648

=0.366