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Let {x}={({0}.{15})}^{{{20}}}{} Find the characteristic and ma

Question

Let $x = (0.15)^{20} ˙$ Find the characteristic and mantissa of the logarithm of $x$ to the base 10. Assume $(lo g)_{10} 2 = 0.301 a n d (lo g)_{10} 3 = 0.477 .$

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Let

x = (0.15)^{20} ˙

Find the characteristic and mantissa of the logarithm of

x

to the base 10. Assume

(lo g)_{10} 2 = 0.301 a n d (lo g)_{10} 3 = 0.477 .

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Text solutionVerified

Solution:

x = (0.15)^{20}

taking log both side

lo g x = lo g (0.15)^{20}

lo g x = 10 lo g (0.15)

20 lo g (\frac{15}{100}) = 20 [lo g 15 - 2]

20 [lo g 5 + lo g 3 - 2]

20 [lo g (\frac{10}{2}) + lo g 3 - 2]

20 [lo g 10 - lo g 2 + lo g 3 - 2]

20 [lo g 3 - lo g 2 - 1]

20 [0.477 - 0.301 - 1]

- 20 \cdot 0.824 = - 16.48

- 17 + (1 - 0.48)

= 17.52

Characteristics=-17
Mantissa=0.52.

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Question Text	Let $x = (0.15)^{20} ˙$ Find the characteristic and mantissa of the logarithm of $x$ to the base 10. Assume $(lo g)_{10} 2 = 0.301 a n d (lo g)_{10} 3 = 0.477 .$
Answer Type	Text solution:1
Upvotes	150