Question

How do you solve `3^(x-1)=81`?

Answer 1

`x=5`

Explanation:

As `3^(x-1)=81`, we have

`x-1=log_(3)81=log_(3)3^4`

= `4log_(3)3=4×1=4`

Hence `x=4+1=5`.

Answer 2

`x= 5`

Explanation:

In this example, the fact that `81` is one of the powers of `3,` allows us to solve this equation using indices. (`3^4 =81`)

If `x^a = x^b " " rArr a = b"`

If the bases are the same then the indices are equal to each other.

`3^(x-1) = 81`
`color(white)(xxxxx)darr`
`color(blue)(3)^color(red)(x-1) = color(blue)(3)^color(red)(4)" the bases are equal"`

`:.color(red)(x-1 = 4)`

`" "x = 5`