Evaluate: `log_(a^2) b-:log_sqrt(a)(b)^2`

Evaluate: log_(2sqrt(3))144

Express the following in exponential form: a) log_(2)32=5 b) log_(sqrt(2))4=4 c) log_(10)0.01=-2

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

The value of (6 a^(log_(e)b)(log_(a^(2))b)(log_(b^(2))a))/(e^(log_(e)a*log_(e)b)) is

The value of "log"_(2)"log"_(2)"log"_(4) 256 + 2 "log"_(sqrt(2))2 , is

Show that the sequence loga ,log((a^2)/b),log((a^3)/(b^2)),log((a^4)/(b^3)), forms an A.P.

Prove that: 2^((sqrt((log)_a4sqrt(a b)+(log)_b4sqrt(a b))-sqrt((log)_a4sqrt(b/a)+(log)_b4sqrt(a/b))))dotsqrt((log)_a b)={2ifbgeqa >1 and 2^(log_a(b) if 1

Prove that : (i) (log a)^(2) - (log b)^(2) = log((a)/(b)).log(ab) (ii) If a log b + b log a - 1 = 0, then b^(a).a^(b) = 10

The value of ("log"_(a)("log"_(b)a))/("log"_(b)("log"_(a)b)) , is