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

Question

1404 views around the world

You can reuse this answer
Creative Commons License

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#