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

Question

1214 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-29T19:15:30

#x=2#

Solution

#9^(x-1)=3^x#

Making bases of both sides equal

As 9 can be written as #9=3^2#

#3^(2(x-1))=3^x#

It must be equal to

#2(x-1)=x#

#2x-2=x#

#2x-x=2#

#x=2#