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If log 2 = .301, find the number of digits in (125)25.
- a)53
- b)50
- c)25
- d)63
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If log 2 = .301, find the number of digits in (125)25.a)53b)50c)25d)63...
logy = 25 log 125
= 25 [log 1000 - 3 log 2]
= 25 x (2.097)
= 52 +
Hence 53 digits.
Hence 53 digits.
Most Upvoted Answer
If log 2 = .301, find the number of digits in (125)25.a)53b)50c)25d)63...
Solution:
We know that,
log a^n = n log a
Given, log 2 = 0.301
We need to find the number of digits in (125)^25
Let's simplify the given expression first.
(125)^25 = (5^3)^25 = 5^75
We know that,
log 5 = 0.699
Therefore,
log 5^75 = 75 log 5 = 75 × 0.699 = 52.425
Now, we need to find the number of digits in 5^75.
To find the number of digits, we use the following formula:
Number of digits = ⌊log x⌋ + 1
where ⌊x⌋ denotes the greatest integer less than or equal to x.
Using this formula, we get:
Number of digits = ⌊log 5^75⌋ + 1
= ⌊52.425⌋ + 1
= 52 + 1
= 53
Therefore, the number of digits in (125)^25 is 53. Hence, the correct option is A.
We know that,
log a^n = n log a
Given, log 2 = 0.301
We need to find the number of digits in (125)^25
Let's simplify the given expression first.
(125)^25 = (5^3)^25 = 5^75
We know that,
log 5 = 0.699
Therefore,
log 5^75 = 75 log 5 = 75 × 0.699 = 52.425
Now, we need to find the number of digits in 5^75.
To find the number of digits, we use the following formula:
Number of digits = ⌊log x⌋ + 1
where ⌊x⌋ denotes the greatest integer less than or equal to x.
Using this formula, we get:
Number of digits = ⌊log 5^75⌋ + 1
= ⌊52.425⌋ + 1
= 52 + 1
= 53
Therefore, the number of digits in (125)^25 is 53. Hence, the correct option is A.
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If log 2 = .301, find the number of digits in (125)25.a)53b)50c)25d)63Correct answer is option 'A'. Can you explain this answer?
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