Question

If log_√27x = 2 `(2)/(3)` , find x.

Answer 1

log_√27x = 2 `(2)/ (3)`

∴ log_√27x =  `(8)/ (3)`

∴ x = `( sqrt27 )^((8)/ (3))`  ...[ ∵ log_a x = b ⇒ x = a^b ]     

∴ x = `( 27^((1)/(2)))^(8/3)` 

∴ x = `( 3 ^((3)/(2)))^(8/3)`

∴ x = `3^((3/2)xx(8/3))`

∴ x = 3⁴ 

∴ x = 81