If Log√27x = 2 (2)/(3) , Find X - Mathematics

If log_√27x = 2 `(2)/(3)` , find x.

Sum

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

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