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

Question

22105 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T08:03:00

$x=5$

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 · 2016-07-15T09:39:37

$x= 5$

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.

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

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

$" "x = 5$

How do you solve 3^(x-1)=813^(x-1)=81?