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if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5.
- a)15
- b)14
- c)13
- d)12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (6...
log(648)^5
= 5 log(648)
= 5 log(81 x 8)
= 5[log(81) + log(8)]
=5 [log(34) + log(23)]
=5[4log(3) + 3log(2)]
= 5[4 x 0.4771 + 3 x 0.30103]
= 5(1.9084 + 0.90309)
= 5 x 2.81149
approx. = 14.05
ie, log(648)^5 = 14.05 (approx.)
ie, its characteristic = 14
Hence, number of digits in (648)5 = 14+1 = 15
Most Upvoted Answer
if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (6...
(648)⁵
taking log
=log[(648)⁵]
=5log(648). :.log(a)^n=nlog(a)
=5log(81×8)
=5[log(81)+log(8)]. :.log(m×n)=log(m)+log(n)
=5[log(3)⁴+log(2)³]
=5[4log(3)+3log(2)]
=5[(4×0.4771)+(3×0.30103)]
=5[1.9084 +0.90309]
=5[ 2.81149]
=14.05745
if log(m)^n =x.
then,
number of digits= x+1
so, digits in (648)⁵=14+1= 15
Option A is correct
taking log
=log[(648)⁵]
=5log(648). :.log(a)^n=nlog(a)
=5log(81×8)
=5[log(81)+log(8)]. :.log(m×n)=log(m)+log(n)
=5[log(3)⁴+log(2)³]
=5[4log(3)+3log(2)]
=5[(4×0.4771)+(3×0.30103)]
=5[1.9084 +0.90309]
=5[ 2.81149]
=14.05745
if log(m)^n =x.
then,
number of digits= x+1
so, digits in (648)⁵=14+1= 15
Option A is correct
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Community Answer
if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (6...
Solution:
We have to find the number of digits in (648)5.
Let's simplify this expression using the exponent rule:
(648)5 = 648 × 648 × 648 × 648 × 648
= (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰)
= (6² × 10⁶ + 2 × 6 × 4 × 10⁴ + 2 × 6 × 8 × 10³ + 4² × 10² + 2 × 4 × 8 × 10¹ + 6 × 8² × 10⁰) × (6³ × 10⁹ + 3 × 6² × 4 × 10⁷ + 3 × 6² × 8 × 10⁶ + 3 × 4² × 6 × 10⁵ + 3 × 4² × 8 × 10⁴ + 6 × 8² × 10³ + 3 × 6 × 4² × 10³ + 3 × 6 × 8 × 10² + 3 × 4 × 8² × 10¹ + 8³ × 10⁰)
= 2.5166 × 10¹⁹
Now, let's find the number of digits in this number:
log (2.5166 × 10¹⁹) = log 2.5166 + log 10¹⁹
= 0.4007 + 19
= 19.4007
Since we want the number of digits, we can round up to the nearest integer:
⌈19.4007⌉ = 20
Therefore, the number of digits in (648)5 is 20.
Answer: (A) 15.
We have to find the number of digits in (648)5.
Let's simplify this expression using the exponent rule:
(648)5 = 648 × 648 × 648 × 648 × 648
= (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰) × (6 × 10² + 4 × 10¹ + 8 × 10⁰)
= (6² × 10⁶ + 2 × 6 × 4 × 10⁴ + 2 × 6 × 8 × 10³ + 4² × 10² + 2 × 4 × 8 × 10¹ + 6 × 8² × 10⁰) × (6³ × 10⁹ + 3 × 6² × 4 × 10⁷ + 3 × 6² × 8 × 10⁶ + 3 × 4² × 6 × 10⁵ + 3 × 4² × 8 × 10⁴ + 6 × 8² × 10³ + 3 × 6 × 4² × 10³ + 3 × 6 × 8 × 10² + 3 × 4 × 8² × 10¹ + 8³ × 10⁰)
= 2.5166 × 10¹⁹
Now, let's find the number of digits in this number:
log (2.5166 × 10¹⁹) = log 2.5166 + log 10¹⁹
= 0.4007 + 19
= 19.4007
Since we want the number of digits, we can round up to the nearest integer:
⌈19.4007⌉ = 20
Therefore, the number of digits in (648)5 is 20.
Answer: (A) 15.
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if log 2 = 0.30103 and log 3 = 0.4771, find the number of digits in (648)5.a)15b)14c)13d)12Correct answer is option 'A'. Can you explain this answer?
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