`log root(3)(1/27)`

But we know that

`root(n)(x) = x^(1/n)`

Hence,

⇒ `log (1/27)^(1/3)`

but `27 = 3^3`

⇒ `log (1/(3^3))^(1/3)`

But also,

`1/(3^3) = (1/3)^3`

Hence,

⇒ `log (1/3)^(3 * 1/3)` = `log (1/3)`

⇒ `log (1/3) = log 3^-1 = -log 3`

From mathematical table,

log 3 `~~` 0.4771

Hence,

⇒ `-log 3 = -0.4771`

∴ `log root(3)(1/27) ~~ -0.4771`

Sorry, it's under construction !

Sorry, it's under construction !