Question

100 points! Please help! ASAP! Please you'll help me a lot!

Answer 1

step 1 :- first of all ,
we see that here
√{(4 - 1/3√2√( 4 -1/3√2).........∞)}
let whole system of this is P

P = √{( 4 -1/3√2√(4-1/3√2)√.....∞) }
here infinte just like same term ,
after first term they are also P { becoz no any effect in infinite term when we do this ,)

so, P = √{(4 -1/3√2)P }
take square both sides
P² = 4 -1/3√2P

3√2P² +P -4.3√2 = 0

3√2P² + P -12√2 = 0

use quadratic formula,

P = { -1 ±√(1 + 288)}/6√2

= { -1 ± 17}/6√2

but P is always positive becoz
P = exponential function .

so, P = (-1 + 17)/6√2 = 8/3√2

now,

= 6 + log{1/3√2×8/3√2 base 3/2 }

= 6 +log{ 4/9 base 3/2 }

= 6 + log { (2/3)^-2 base (3/2) }

= 6 -2

=4 ( answer )

Answer 2

I know this answer!!!

Hope This Helps You!