Okay, the first thing to do is recall properties of exponents and how to rewrite number as a single base. What this means is if you were to rewrite 36, you could rewrite it as: 62.
Additionally if you have 81x. Then you could rewrite as either a base of 9 or a base of 3.
recall that 81=92 so 81x=(92)x : from here properties of exponents tell you to multiply the exponents together, so you get: 81x=92x
If you follow the same process further you will have: 34x.
With this you may look at:
9x+1=27x-1 and you may see that 9 and 27 can both be rewritten as the same base. Where:
9=32 and 27=33
Making the substitutions:
Remember that the exponents multiply. But more importantly, since you have the same base, you may set the exponents equal to one another:
32(x+1)=33(x-1) can only be true if the exponents are the same:
Distributing and solving:
You may check your answer to see if this is correct and you find that it is the solution to the exponential.