Question

Log3+log9+log27+log81+...... Question: how many terms of the section log2187?

Answer 1

7th term.

Explanation:

The given series is

`\log 3+\log 9+\log 27+\log 81+...`

We need to find the number of term log 2187.

Here, terms inside the log are 3, 9, 27, 81, ... are in G.P.

First term = 3

Common ratio
`=(9)/(3)=3`

nth term of a G.P. is

`a_n=ar^(n-1)`

where, a is first term and r is common ratio.

`2187=3(3)^(n-1)`

Divide both sides by 3.

`729=(3)^(n-1)`

`3^6=(3)^(n-1)`

On comparing both sides, we get

`n-1=6`

`n=7`

Since 7th term of the G.P. 3, 9, 27, 81, ... is 2187, therefore, 7th term of
`\log 3+\log 9+\log 27+\log 81+...` is log 2187.