How to solve for x?
1/9 = 27x+1
We can express both 1/9 and 27 as powers of 3 .
1/32 = (33)x+1
3-2 = (33)x+1
Since (xa)b = xab , (33)x+1 = 33(x + 1) = 33x + 3
3-2 = 33x+3
The bases now equal, so we can equate the exponents.
-2 = 3x + 3
-5 = 3x
-5/3 = x