Prove the identity; `(log)_a N* (log)_b N+(log)_b N * (log)_c N+(log)_c N * (log)_a N=((log)_a N*(log)_b N*(log)_c N)/((log)_(a b c)N)`

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

Compute the following a^(((log)_b((log)_a N))/((log)_b(log a)))

Solve for x :(log)_4(log)_3(log)_2x=0

Statement I: If a=y^2,\ b=z^2, c=x^2,\ t h e n8(log)_a x^3dot(log)_b y^3dot(log)_c z^3=27 Statement II: (log)_b adot(log)_c b=(log)_c a ,\ also (log)_b a=1/("log"_a b) Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1. Statement 1 is true, Statement 2 is true;2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true

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

For positive numbers x ,\ y\ a n d\ z the numerical value of the determinant |1(log)_x y(log)_x z(log)_y x1(log)_y z(log)_z x(log)_z y1| is- a. 0 b. logx y z c. "log"(x+y+z) d. logx\ logy\ logz

Prove that (log)_7 10 is greater than (log)_(11)13.

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)

int (dx)/(x log x log (logx))=...

Solve the system of equations: (log)_a x(log)_a(x y z)=48, (log)_a y log_a(x y z)=12 , a >0,\ a!=1(log)_a z log_a(x y z)=84\