`a log_a1+2log_a 2+3log_a 3+.........+n log_a n=2^2. 3^3. 4^4..........n^n`

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x_1) [log_(x _2) {log_(x_3).........log_(x_n) (x_n)^(x_(r=i))}]

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x_1) [log_(x _2) {log_(x_3).........log_(x_n) (x_n)^(x_(r=i))}]

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x_1) [log_(x _2) {log_(x_3).........log_(x_n) (x_n)^(x_(r=i))}]

If x_n > x_(n-1) > ..........> x_3 > x_1 > 1. then the value of log_(x1) [log_(x2) {log_(x3).........log_(x4) (x_n)^(x_(r=i))}]

2(log a+log a^(2)+log a^(3)+log a^(4)+............+log a^(n)) is equal to

If ngt1 then prove that 1/(log_2 n )+1/(log_3 n)+.................+1/log_(53) n =1/(log_(53!) n

The value of log_(b)a+log_(b^(2))a^(2) + log_(b^(3))a^(3) + ... + log_(b^(n))a^(n)

If log2,log(2^n-1) and log(2^n+3) are in A.P. then n =

Prove that : (vi) log_(a)x + log_(a^2)x^(2) + log_(a^3)x^(3) + ………….+ log_(a^n)x^(n) = log_(a)x^(n)

The sum of the series log_(a)b+log_(a^(2))b^(2)+log_(a^(3))b^(3)+....log_(a^(n))b^(n)