If `(log)_(10)5=aa n d(log)_(10)3=b ,t h e n` `(A) (log)_(30)8=(3(1-a))/(b+1)` `(B) (log)_(40)15=(a+b)/(3-2a)` `(C) (log)_(243)32=(1-a)/b` (d) none of these

if log_10 5=a and log_10 3=b then:

If (log)_a3=2 and (log)_b8=3 , then prove that (log)_a b=(log)_3 4.

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

If (log)_(10)[1/(2^x+x-1)]=x[(log)_(10)5-1] , then x= 4 (b) 3 (c) 2 (d) 1

The value of 3^((log)_4 5)-5^((log)_4 3) is 0 (b) 1 (c) 2 (d) none of these

If (log)_(10)2=a ,(log)_(10)3=bt h e n(log)_(0. 72)(9. 6) in terms of a and b is equal to (a) (2a+3b-1)/(5a+b-2) (b) (5a+b-1)/(3a+2b-2) (c) (3a+b-2)/(2a+3b-1) (d) (2a+5b-2)/(3a+b-1)

If log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4 .

If y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

(log)_(x-1)x (log)_(x-2)(x-1) (log)_(x-12)(x-11)=2,x is equal to: 9 (b) 16 (c) 25 (d) none of these

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)