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)_(a)3=2and(log)_(b)8=3, then prove that (log)_(a)b=(log)_(3)4

If log_(10)2=a backslash and log_(10)3=b, then log_(5)12 equals a.(a+b)/(1+a) b.(2a+b)/(1+a) c.(a+2b)/(1+a)d(2a+b)/(1-a)

"If" ("log"_(10)a)/(2) = ("log"_(10)b)/(3) = ("log"_(10)c)/(5) , then bc =

The value of 3^(log_(4)5)-5^(log_(4)3) is 0(b)1(c)2(d) none of these

If log15=a and log75=b, then log_(75)45 is: (3b-a)/(a)( b) (b-3a)/(a)(3a-b)/(b) (d) (a-3b)/(b)

Prove that ((log)_(a)N)/((log)_(ab)N)=1+(log)_(a)b

Given system of simultaneous equations 2^x . 5^y=1 a n d 5^(x+1). 2^y=2. Then - a.x=(log)_(10)5 a n d y=(log)_(10)2 b. x=(log)_(10)2 a n d y=(log)_(10)5 c. x=(log)_(10)(1/5) a n d y=(log)_(10)2 d. x=(log)_(10)5 a n d y=(log)_(10)(1/2)

The value of 3^((log)_4 5)+4^((log)_5 3)-5^((log)_4 3)-3^((log)_5 4) is- a.0 b. 1 c.2 d. none of these

The values of the constants a , ba n dc for which the function f(x)={(1+a x)^(1//x)b ,x 0x=0 may be continuous at x=0, are a=(log)_e(2/3),b=-2/3,c=1 a="log")e (2/3),b2/3,c=-1 a=(log)_e(2/3),b=2/3,c=1 (d) none of these