Prove that `2^{{sqrt(log_a 4sqrtab + log_b 4sqrtab)-sqrt((log_a)4sqrt(b/a)+log_b 4sqrt(a/b))}sqrt(log_a b))= { 2 , b gea gt1`and `2^(log_b a) , 1 ltblta`

Prove that 2^{{sqrt(log_a 4sqrtab + log_b 4sqrtab)-sqrt((log_a)4sqrt(b/a)+log_b 4sqrt(a/b))}sqrt(log_a b))= { 2 , b gea gt1and 2^(log_b a) , 1 ltblta

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

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

Prove that: 2^(sqrt((log)_(a)4sqrt(ab)+(log)_(b)4sqrt(ab))-(log)_(a)4sqrt((b)/(a))+(log)_(b)4sqrt((pi)/(b)))sqrt((log)_(a)b)={2quad if b>=a>1 and 2^(log_(a)(b)) if 1

Prove that a sqrt(log_(a)b)-b sqrt(log_(b)a)=0

log_(2)sqrt(x)+log_(2)sqrt(x)=4

2^((sqrt(log_a(ab)^(1/4)+log_b(ab)^(1/4))-sqrt(log_a(b/a)^(1/4)+log_b(a/b)^(1/4)))sqrt(log_a(b)) =

2^((sqrt(log_a(ab)^(1//4)+log_b(ab)^(1//4))-sqrt(log_a(b/a)^(1//4)+log_b(a/b)^(1//4))) sqrt(log_a(b)) =

2^((sqrt(log_a(ab)^(1//4)+log_b(ab)^(1//4))-sqrt(log_a(b/a)^(1//4)+log_b(a/b)^(1//4))) sqrt(log_a(b)) =