If `((log)_a N)/((log)_c N)=((log)_a N-(log)_b N)/((log)_b N-(log)_c N),` where `N >0` and `N!=1, a , b , c >0,!=1`, then prove that `b^2=a c`

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)))

If (log)_b a(log)_c a+(log)_a b(log)_c b+(log)_a c(log)_bc=3 (where a , b , c are different positive real numbers !=1), then find the value of a b c .

log (log_(ab) a +(1)/(log_(b)ab)) is (where ab ne 1)

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

If a^x=b , b^y=c ,c^z=a and x=(log)_b a^2, y=(log)_c b^3,z=(log)_a c^k , where a,b, c >0 and a , b , c!=1 then k is equal to a. 1/5 b. 1/6 c. (log)_(64)2 d. (log)_(32)2

If x=1+(log)_a b c , y=1+(log)_b c a and z=1+(log)_c a b , then prove that x y z=x y+y z+z x

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

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)

The value of N satisfying (log)_a[1+(log)_b\ {1+(log)_c(1+(log)_p N)}]=0 is- a. 4 b. 3 c. 2 d. 1