Explain the graph of a function

Question

Consider this function 9^2x-1 = 27. Using graphs of exponents, give a graphical interpretation of what it means to find the x values which satisfy the equation above.

Answer 1

9^2x-1 = 27

(3²)^2x-1 = 3³

3^4x-2 = 3³

Graphing the exponents as y = 4x - 2 and y = 3, we get:

The solution is the intersection of these lines which occurs at x = 5/4