Number of cyphers after decimal before a significant figure starts in ((3/2))-100, is [Given: log 10 2=0.3010 and log 10 3=0.4771 ]

Question

Number of cyphers after decimal before a significant figure starts in ((3/2))-100, is <ve/>[Given: log 10 2=0.3010 and log 10 3=0.4771 ] (A) 16 (B) 17 (C) 18 (D) 19

Tardigrade Admin · Accepted Answer

Let N =((3/2))-100 ∴ log N=100[ log 3- log 2]=-100[0.4771-0.3010]=-100 × 0.1761=-17.61 ∴ Number of cyphers after decimal before a significant figure starts in ((3/2))-100, is |-18|-1=17

Q. Number of cyphers after decimal before a significant figure starts in $(\frac{3}{2})^{- 100}$ , is [Given: $lo g_{10} 2 = 0.3010$ and $lo g_{10} 3 = 0.4771$ ]

16

17

18

19

Let $N = (\frac{3}{2})^{- 100}$
$∴ lo g N = 100 [lo g 3 - lo g 2] = - 100 [0.4771 - 0.3010] = - 100 \times 0.1761 = - 17.61$
$∴$ Number of cyphers after decimal before a significant figure starts in $(\frac{3}{2})^{- 100}$ , is $∣ - 18∣ - 1 = 17$

Q. Number of cyphers after decimal before a significant figure starts in (23​)−100, is [Given: log10​2=0.3010 and log10​3=0.4771 ]

16

17

18

19

Let N=(23​)−100 ∴logN=100[log3−log2]=−100[0.4771−0.3010]=−100×0.1761=−17.61 ∴ Number of cyphers after decimal before a significant figure starts in (23​)−100, is ∣−18∣−1=17

Q. Number of cyphers after decimal before a significant figure starts in $(\frac{3}{2})^{- 100}$ , is [Given: $lo g_{10} 2 = 0.3010$ and $lo g_{10} 3 = 0.4771$ ]

Let $N = (\frac{3}{2})^{- 100}$
$∴ lo g N = 100 [lo g 3 - lo g 2] = - 100 [0.4771 - 0.3010] = - 100 \times 0.1761 = - 17.61$
$∴$ Number of cyphers after decimal before a significant figure starts in $(\frac{3}{2})^{- 100}$ , is $∣ - 18∣ - 1 = 17$