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Find the value of [log2 100]+[log3 99]+[log4 98]+[log5 97]+....+[log100 2] where [X] equals the largest integer less than or equal to X.
Correct answer is '65'. Can you explain this answer?
Most Upvoted Answer
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2]...
[log2 100] = 6 since 26 = 64
Similarly,
[log3 99] = 4
[log4 98] = 3
From [log5 97] to [log9 93], we get 2 each.
From [log10 92] to [log51 51], we get 1. For the rest we get 0.
Hence, sum = 6 + 4 + 3 + 5 x 2 + 42 x 1 = 65
Similarly,
[log3 99] = 4
[log4 98] = 3
From [log5 97] to [log9 93], we get 2 each.
From [log10 92] to [log51 51], we get 1. For the rest we get 0.
Hence, sum = 6 + 4 + 3 + 5 x 2 + 42 x 1 = 65
Community Answer
Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2]...
Explanation:
To find the value of [log2100] [log399] [log498] [log597] .... [log100 2], we need to find the largest integer less than or equal to the logarithm of each number and then multiply them together.
Let's break down the solution step by step:
Step 1: Calculate the logarithm of each number
- [log2100] = log2(100) = 6.64 (approx.)
- [log399] = log3(99) = 4.62 (approx.)
- [log498] = log4(98) = 3.93 (approx.)
- [log597] = log5(97) = 3.14 (approx.)
- [log696] = log6(96) = 2.75 (approx.)
- [log795] = log7(95) = 2.38 (approx.)
- [log894] = log8(94) = 2.04 (approx.)
- [log993] = log9(93) = 1.72 (approx.)
- [log1092] = log10(92) = 1.42 (approx.)
- [log1191] = log11(91) = 1.14 (approx.)
- [log1290] = log12(90) = 0.88 (approx.)
- [log1389] = log13(89) = 0.64 (approx.)
- [log1488] = log14(88) = 0.42 (approx.)
- [log1587] = log15(87) = 0.20 (approx.)
- [log1686] = log16(86) = 0 (since log16(86) is less than 1)
Step 2: Find the largest integer less than or equal to each logarithm
- [log2100] = 6
- [log399] = 4
- [log498] = 3
- [log597] = 3
- [log696] = 2
- [log795] = 2
- [log894] = 2
- [log993] = 1
- [log1092] = 1
- [log1191] = 1
- [log1290] = 0
- [log1389] = 0
- [log1488] = 0
- [log1587] = 0
- [log1686] = 0
Step 3: Multiply the obtained values together
6 * 4 * 3 * 3 * 2 * 2 * 2 * 1 * 1 * 1 * 0 * 0 * 0 * 0 * 0 = 0
Therefore, the value of [log2100] [log399] [log498] [log597] .... [log100 2] is 0.
To find the value of [log2100] [log399] [log498] [log597] .... [log100 2], we need to find the largest integer less than or equal to the logarithm of each number and then multiply them together.
Let's break down the solution step by step:
Step 1: Calculate the logarithm of each number
- [log2100] = log2(100) = 6.64 (approx.)
- [log399] = log3(99) = 4.62 (approx.)
- [log498] = log4(98) = 3.93 (approx.)
- [log597] = log5(97) = 3.14 (approx.)
- [log696] = log6(96) = 2.75 (approx.)
- [log795] = log7(95) = 2.38 (approx.)
- [log894] = log8(94) = 2.04 (approx.)
- [log993] = log9(93) = 1.72 (approx.)
- [log1092] = log10(92) = 1.42 (approx.)
- [log1191] = log11(91) = 1.14 (approx.)
- [log1290] = log12(90) = 0.88 (approx.)
- [log1389] = log13(89) = 0.64 (approx.)
- [log1488] = log14(88) = 0.42 (approx.)
- [log1587] = log15(87) = 0.20 (approx.)
- [log1686] = log16(86) = 0 (since log16(86) is less than 1)
Step 2: Find the largest integer less than or equal to each logarithm
- [log2100] = 6
- [log399] = 4
- [log498] = 3
- [log597] = 3
- [log696] = 2
- [log795] = 2
- [log894] = 2
- [log993] = 1
- [log1092] = 1
- [log1191] = 1
- [log1290] = 0
- [log1389] = 0
- [log1488] = 0
- [log1587] = 0
- [log1686] = 0
Step 3: Multiply the obtained values together
6 * 4 * 3 * 3 * 2 * 2 * 2 * 1 * 1 * 1 * 0 * 0 * 0 * 0 * 0 = 0
Therefore, the value of [log2100] [log399] [log498] [log597] .... [log100 2] is 0.
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Find the value of [log2100]+[log399]+[log498]+[log597]+....+[log100 2] where [X] equals the largest integer less than or equal to X.Correct answer is '65'. Can you explain this answer?
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