Question

What is the value of log ⁡ 5 5 4

Answer 1

`(1)/(4)`

Explanation:

using the rule of logarithms

`log_(b)` x = n ⇒ x =
`b^(n)`

also the rule of exponents/ radicals

`\sqrt[n]{a^(m) }` =
`a^{(m)/(n) }`

let

`log_(5)`
`\sqrt[4]{5}` = n , then

`\sqrt[4]{5}` =
`5^(n)` , that is

`5^{(1)/(4) }` =
`5^(n)`

since bases on both sides are the same, both 5 , then equate the exponents

n =
`(1)/(4)` ( = 0.25 )