If `log_(b)2=a` and `log_(b)5=c` ,where `b>0` with `b!=1`, then `log_(b)500` is equal to which of the following

If x=log_(a)(bc),y=log_(b)(ca)" and "z=log_(c)(ab) , then which of the following is equal to 1 ?

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 log_(10) 2 = a, log_(10)3 = b" then "log_(0.72)(9.6) in terms of a and b is equal to

If log_(a)b=2,log_(b)c=2 and log_(3)c=log_(3)a+3, then (a+b+c) is equal to 93(b)102(c)90(d)243

If log_(4)5=a and log_(5)6=b, then log_(3)2 is equal to (1)/(2a+1) (b) (1)/(2b+1)(c)2ab+1(d)(1)/(2ab-1)

If x=log_(k)b=log_(b)c=(1)/(2)log_(c)d, then log_(k)d is equal to

If log_(3)x=a and log_(7)x=b, then which of the following is equal to log_(21)x?ab(b)(ab)/(a^(-1)+b^(-1))(1)/(a+b)(d)(1)/(a^(-1)+b^(-1))

Solve :2log_(x)a+log_(ax)a+3log_(b)a=0 where a>0,b=a^(2)x

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