If `log_e(1/(2)(a+b))=1/2(log_e a+log_e b),` then `a/(3b)`=

If log_(e)((a+b)/(2))=(1)/(2)(log_(e)a+log_(e)b), then find the relation between a and b.

if log_(e)(x-1) + log_(e)(x) + log_(e)(x+1)=0 , then

log_(2)(1+(1)/(a))+log_(2)(1+(1)/(b))+log_(2)(1+(1)/(c))=2 where a,b,c are three different positive integers, then that log_(e)(a+b+c)=log_(e)a+log_(e)b+log_(e)c or prove that a=1,b=2,c=3.

The value of (6a^((log)_e b)((log)_(a^2)b)((log)_(b^2)a)/(e^((log)_e a(log)_e b))i s independent of a (b) independent of b dependent on a (d) dependent on b

A value of C for which the conclusion of Mean Value Theorem holds for the function f(x)""=""(log)_e x on the interval [1, 3] is (1) 2(log)_3e (2) 1/2""(log)_e3 (3) (log)_3e (4) (log)_e3

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)

Suppose 1 lt a lt sqrt(e) and log_(e)a^(2)+(log_(e)a^(2))^(2)+(log_(e)a^(2))^(3)+…. =3 [log_(e)a+(log_(e)a)^(2)+(log_(e)a)^(3)+…]" (1)" then log_(e)(a^(3))=

If (dy)/(dx)-y log_(e) 2 = 2^(sin x)(cos x -1) log_(e) 2 , then y =

If log_(e) (x^(4) y) = a and log_(e) (x^(2) y^(2)) = b, then log_(e) sqrt(y) in terms of a and b is