Question

Find the value of x in 81^x=1/3?​

Answer 1

x = -
`(1)/(4)`

Explanation:

Using the rules of exponents

`(a^m)^(n)` =
`a^(mn)` ,
`a^(-m)` =
`(1)/(a^(m) )`

Given

`81^(x)` =
`(1)/(3)` [ note that 81 =
`3^(4)` ] , then

`(3^4)^(x)` =
`3^(-1)` , that is

`3^(4x)` =
`3^(-1)`

Since the bases on both sides are equal, both 3, then equate exponents

4x = - 1 ( divide both sides by 4 )

x = -
`(1)/(4)`

Answer 2

x = -1/4

Explanation:

`81^(x)` = 1/3

`3^(4)^(x)` =
`3^(-1)`

4x = -1

x = -1/4