Question

2(log a+log a^2+log a^3..........log a^n) = ?

i'll mark who ever gives the correct answer as the brainliest

Answer 1

Answer:

Step-by-step explanation:

2(log a + log a^2 + log a^3..................log a^n)

= 2( log a*a^2 + log a^3...........log a^n)  [ log a + log b = log ab]

= 2(log a^3 + log a^ 3 ...........log a^n)

= 2 (log a^3 * a^3 .........log a^n)

= 2 (log a^6.........log a^n)

= pattern continues

(sum of first n natural numbers = n(n+1)/2

= 2 (log a ^n(n+1)/2)

= 2(1/2log a^n(n+1))

= log a^n(n+1)

= n(n+1) log a