I dont remember how to do this problem and being summer, I dont have my textbook to help.
Solve: 4^(x+2)=9^(x-1)
Whatever base you choose, the rules are the same
denotes the natural logarithm and is like an *universal* base :
Continuing from :
Group the x together :
Now, if you take the logarithm in base 2, you'll have because . Actually, it's .
But in a common logarithm, you have :
, same goes for
Substituting in (1) :
Simplify by 2 :
You gotta learn how to use the natural logarithm. Using bases just sometimes avoid difficulties things easier, but in exercises like this one, it brings difficulties !