Which is smaller? `2` or `((log)_("e"-1)2+(log)_2(e-1))`

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8\ a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_3 8 (log)_3 8 > log_3 6 (log)_2 6 > log_3 6 (log)_4 6 < log_3 6

Comprehension 2: In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8 and (log)_(1/2)4 is larger than (log)_(1/2)8 and (log)_(2/3)5/6 is- a. less than zero b. greater than zero and less than one c. greater than one d. none of these

Solve (log)_x2(log)_(2x)2=(log)_(4x)2.

Find all real numbers x which satisfy the equation 2(log)_2log\ _2x+(log)_(1/2)(log)_2(2sqrt(2)x)=1.

The number of solutions of (log)_4(x-1)=(log)_2(x-3) is (2001, 2M) (a) 3 (b)1 (c) 2 (d) 0

Solve : (log)_((2"x"-1))\ ((x^4+2)/(2x+1))\ =1

Find the domain of f(x)=(log)_(10)(log)_2(log)_(2/pi)(t a n^(-1)x)^(-1)

((log)_(10)(x-3))/((log)_(10)(x^2-21))=1/2

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

Given a^2+b^2=c^2, a >0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ prove that : (log)_("c"+"b")a+(log)_("c"-"b")a=2(log)_("c"+"b")adot(log)_("c"-"b")a