`a^(log_b c)=c^(log_b a)`

a^(log b-log c)*b^(log c-log a)*c^(log a-log b) has a value of :

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

If (a^(log_b x))^2-5 a^(log_b x)+6=0, where a >0, b >0 & a b!=1, then the value of x can be equal to (a) 2^(log_b a) (b) 3^(log_a b) (c) b^(log_a2) (d) a^(log_b3)

If a,b,c are positive reral numbers such that (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then prove that

Let ABC be a triangle right at C. The value (log_(b+c)a+log_(c-b)a)/(log_(b+c)a*log_(c-b)a)(b+c!=1,c-b!=1) equals

If a,b,c gt1 then Delta=|(log_(a)(abc),log_(a)b,log_(a)c),(log_b(abc),1,log_(b)c),(log_(c)(abc),log_(c)b,1)| equals

If (log_a N)/(log_c N)=(log_a N-log_b N)/(log_b N-log_c N) where N>0 and N!=1 a,b,c>0 and not equal to 1 , then prove that b^2=ac

Assuming that all logarithmic terms are define which of the following statement(s) is/are incorrect? (A)log_b(ysqrtx)=log_b y.(1/2log_b x) , (B) log_b x-log_b y=(log_b x)/(log_b y) , (C)2(log_b x+log_b y)=log_b (x^2y^2) , (D) 4log_b x-log_b y=log(x^4/y^-3)

If (log a)/(b-c)=(log b)/(c-a)=(log c)/(a-b), then a^(b+c)*b^(c+a)*c^(a+b)=