+0  
 
0
75
1
avatar

If 10^{2n} < 25,000,000 < 10^{2n + 1}, what is the integer value of n?

 Jul 23, 2022
 #1
avatar+124676 
+1

 

10 ^(2n)  < 25000000  take the log of  both sides

 

log 10^(2n)  < log ( 25000000)

 

(2n)  < log (25000000)  / log 10                    (log 10 =  1)

 

2n < log (25000000)

 

n<  log (25000000) / 2   ≈   3.698   →    n <  ≈ 3.698

 

Similarly we would have

 

log (25000000) < 10^( 2n + 1)

 

[ log (25000000) - 1] / 2  < n  →     n >   ≈  3.19

 

The integer value of n =  3

 

cool cool cool

 Jul 23, 2022

13 Online Users

avatar