What's the formula to solve summation of logarithms? I'm studying summation. Everything I know so f

ttyme411gl

ttyme411gl

Answered question

2022-07-10

What's the formula to solve summation of logarithms?
I'm studying summation. Everything I know so far is that:
i = 1 n   k = n ( n + 1 ) 2  
i = 1 n   k 2 = n ( n + 1 ) ( 2 n + 1 ) 6  
i = 1 n   k 3 = n 2 ( n + 1 ) 2 4  
Unfortunately, I can't find neither on my book nor on the internet what the result of:
i = 1 n log i
i = 1 n ln i
is.
Can you help me out?

Answer & Explanation

Alexis Fields

Alexis Fields

Beginner2022-07-11Added 14 answers

By using the fact that
log a + log b = log a b
then
n log i = log ( n ! )
n ln i = ln ( n ! )
Ciara Mcdaniel

Ciara Mcdaniel

Beginner2022-07-12Added 4 answers

Since log ( A ) + log ( B ) = log ( A B ), then i = 1 n log ( i ) = log ( n ! ). I'm not sure if this helps a lot since you have changed a summation of n terms into a product of n factors, but it's something.

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