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Answer:
n = 99
Step-by-step explanation:
The sum of logarithms is the log of a product. Here, the sum of terms is ...
log(2/1) +log(3/2) +log(4/3) + ... +log((n+1)/n)
= log((2/1)(3/2)(4/3)×...×((n+1)/n)) = log(n+1)
So, the question reduces to ...
log(n+1) = 2
Taking antilogs, we have ...
n +1 = 10^2 = 100
n = 99
The value of n that makes the sum 2 is 99.
Answers
1. x=7
2. x=6
3. x=9
4. x=8
Explanations
1. This is an isosceles triangle because two angles are congruent. This also means the two sides are the same. This means 7 = x.
2. This is an equilateral triangle because all the angles are the same. Therefore, all sides are also the same. So x = 6.
3. This is also an equilateral triangle. We know this because all sides are the same. So from this we know that x-3 = 6. Solve the equation, and you'll find that x = 3.
4. This is also an isosceles triangle, because two of the angles are congruent. This means 2x-9 = 7. Solve this equation; x=8
I got 3.333... and nice hand writing
