Question

If log 2 = 0.3010, log 3 = 0.4771, find the value of log
$\sqrt{120}$
​

Answer 1

log  $\sqrt{120}$ = 1.038

Step-by-step explanation:

log  $\sqrt{120}$ = $\frac{1}{2}$ log 120                      // peoperty used log(xⁿ) = n log (x)

0.5* log (120) = (0.5 ) log(12*10)                 // log (a*b) = log (a)+log (b)

           =  (0.5 ) { log 12 +log 10   }                   // log 10 = 1

           =  (0.5 ) { log(3*2*2) + 1   }         // log (a*b*c) = log (a)+log (b)+log (c)

          = (0.5 ) { log 3 +log 2+log 2 + 1 }

          =0.5 *  { 0.3010+0.3010+0.4771+1 }

        =                       1.038