Let `x=(0. 15)^(20)dot` Find the characteristic and mantissa of the logarithm of `x` to the base 10. Assume `(log)_(10)2=0. 301a n d(log)_(10)3=0. 477.`

Explanation

`x=(0.15)^20`

taking log both side

`logx=log(0.15)^20`

`logx=10log(0.15)`

`20log(15/100)=20[log15-2]`

`20[log5+log3-2]`

`20[log(10/2)+log3-2]`

`20[log10-log2+log3-2]`

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