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Let x=(0. 15)^(20)dot Find the character...

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.`

Text Solution

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` log x = log(0.15)^(20)= 20 log (15/100)`
` = 20 [log 15-2]`
` = 20[ log 3+log 5-2]`
` = 20[log 3+1-log 2 - 2]" "(.:' log_(10) 5 = log_(10) 10/2)`
`=20[-1+log 3 - log 2]`
` =20 [ -1+0.477-0.301]`
` =- 20 xx 0.824`
` =- 16.48`
` = bar(17).52`
Hence, Characteristic =- 17 and Mantissa = ` 0.52`
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Knowledge Check

  • The number of digits in 20^(301) (given log_(10)2=0.3010) is

    A
    602
    B
    301
    C
    392
    D
    391

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