If `log_nm=1/a: log_pm=1/b; log_rm=1/c`, then the value of `log_(npr) m` is

If log_(a)b=1/2,log_(b)c=1/3" and "log_(c)a=(K)/(5) , then the value of K is

If a>1,b>1, then the minimum value of log_(b)a+log_(a)b is

If a > 1, b > 1, then the minimum value of log_b a + log_a b is

If p>1 and q>1 are such that log(p+q)=log p+log q ,then the value of log(p-1)+log(q-1) is equal to (a)0(b)1 (c) 2(d) none of these

If log 25 = a " and " log 225 = b , then find the value of log ((1/9)^(2)) + log (1/(2250)) in terms of a and b (base of the log is 10 everywhere).

If a,b,c are non-zero and different from 1, then the value of |{:( log _(a) 1 , log _(a) b , log _(a) c ), ( log _(a ) ((1)/(b)), log _(b) 1 ,log_(a) ((1)/(c))), ( log _(a) ((1)/(c)) ,log _(a)c, log _(c) 1):}| is

Let a,b" and "c are distinct positive numbers,none of them is equal to unity such that log _(b)a .log_(c)a+log_(a)b*log_(c)b+log_(a)c*log_(b)c-log_(b)a sqrt(a)*log_(sqrt(c))b^(1/3)*log_(a)c^(3)=0, then the value of abc is -

l=1+log_(a)bc,m=1+log_(b)ca,n=1+log_(c)a then the value of (1)/(l)+(1)/(m)+(1)/(n)-1

Let a=(log_(27)8)/(log_(3)2),b=((1)/(2^(log_(2)5)))((1)/(5^(log_(5)(01)))) and c=(log_(4)27)/(log_(4)3) then the value of (a+b+c), is and c=(log_(4)27)/(log_(4)3)