How do you solve #243=9^(2x+1)#?
It really is an advantage to know all the powers up to 1000.
You will then recognise that
Without knowing this, you will have to resort to finding the prime factors. Another clue is that
So this is an exponential equation with 3 as the base,
The bases are equal, so the indices must be equal.
On inspection we see that LHS,
Similarly on RHS,
Thus the equation becomes
Since bases on both sides are equal, therefore for the equation to be true, powers must be equal.