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

Compute the following (81^(1/((log)_5 9))+3^(3/((log)_(sqrt(6))3)))/(409)dot((sqrt(7))^(2/((log)_(25)7))-(125)^((log)_(25)6))

Compute the following 56+(log)_(sqrt(2))4/(sqrt(7)+sqrt(3))+(log)_(1//2)1/(10+2sqrt(21))

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

Expand the following. log(128/625)

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 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)

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

Differentiate the following w.r.t.x. log_(10)x+log_(x)10+log_(x)x+log_(10)10

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

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