How do you solve $1/81 - 9^(x-3) = 0$ ?

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Answer 1 · 2015-09-24T05:01:30

$color(blue)(x=1$

$1/81 - 9^(x-3) = 0$

We know that , $1/81= 1/9^2$

As per property
$color(blue)(a^-m = 1/a^m$

So,
$1/81= 1/9^2 = 9^-2$

The expression now becomes:

$1/9^2 - 9^(x-3) = 9^-2 - 9^(x-3) =0$

$9^color(blue)(-2) =9^color(blue)((x-3)$

As the bases are equal we can equate the powers:

$-2 = x-3$

$x= -2+3$

$color(blue)(x=1$

How do you solve 1/81 - 9^(x-3) = 01/81 - 9^(x-3) = 0?