`log_a n+ log_n a+ log_a a`=

STATEMENT-1 : If a, b, c are distinct positive reals in G.P. then log_(a) n, log_(b) n, log_(c) n are in H.P. , AA n ne N and STATEMENT-2 : The sum of reciprocals of first n terms of the series 1 + (1)/(3) + (1)/(5) + (1)/(7) + (1)/(9) + ..... "is" n^(2) and

Assuming that log (mn) = log m + logn prove that log x^(n) = n log x, n in N

Prove that: log_a x=log_bx xx log_c b xx…xx log_n m xx log_a n

if (1+3+5-...upto n terms)/(4+7+10+...upto n terms)=20/(7log_10 X and n = log_10 x + log_10 X^1/2 + log_10 X^1/4 + ............ + oo , then x is equal to

Find the area bounded by y=log_e x , y=-log_e x ,y=log_e(-x),a n dy=-log_e(-x)dot

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

If log_(b) n = 2 and log_(n) 2b = 2 , then find the value of b.

1/(1+log_b a+log_b c)+1/(1+log_c a+log_c b)+1/(1+log_a b+log_a c)

State, true or false : (i) log 1 xx log 1000 = 0 (ii) (log x)/(log y) = log x - log y (iii) If (log 25)/(log 5) = log x , then x = 2 (iv) log x xx log y = log x + log y

If ((log)_a N)/((log)_c N)=((log)_a N-(log)_b N)/((log)_b N-(log)_c N),w h e r eN >0a n dN!=1, a , b , c >0 and not equal to 1, then prove that b^2=a c