`y =log_ a n +log_ n a +log_ a a`

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

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

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

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) .

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

If in an AP, t_1 = log_10 a, t_(n+1) = log_10 b and t_(2n+1) = log_10 c then a, b, c are in

If x=log_(2a) a,y=log_(3a) 2a and z=log_(4a) 3a then prove that xyz+1=2yz

Given log x = m + n and log y = m - n, express the value of "log" (10 x)/(y^(2)) in terms of m and n.

Prove the identity; (log)_a Ndot(log)_b N+(log)_b Ndot(log)_c N+(log)_c Ndot(log)_a N=((log)_a Ndot(log)_b Ndot(log)_c N)/((log)_(a b c)N)

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