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

ttyme411gl

ttyme411gl

Answered

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

Expert

2022-07-11Added 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

Expert

2022-07-12Added 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.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?