Question

if log2 =0.3010 and log 3 =0.4771 then find log (0.0036) ^1/4

Answer 1

Hi ,

It is given that ,

log 2 = 0.3010 ,

log 3 = 0.4771 ,

log ( 0.0036 )^1/4

= log ( 36/10⁴ )^1/4

= log 36^1/4 - log ( 10⁴ )^1/4

[ Since ,

log ( m/n ) = log m - log n ]

= log ( 6² )^1/4 - log 10

= log √6 - 1

[ Since log 10 ( base 10 ) = 1 ]

= log 6½ - 1

= 1/2 log 6 - 1

[ Since log a^m = m log a ]

= 1/2 log ( 2 × 3 ) - 1

= 1/2 [ log 2 + log 3 ] - 1

[ Since ,

log mn = log m + log n ]

= 1/2 [ 0.3010 + 0.4771 ] - 1

= 1/2 × 0.7781 - 1

= 0.38905 - 1

= - 0.61095

I hope this helps you.

: )