To solve this equation, we'll first apply the product rule of logarithms which states that loga (m) + loga (n) = loga (m*n).

So, we can rewrite the equation as:

log5 (7x + 4) = log5 (2x – 1) + 1

Now, we'll combine the two logarithms on the right side using the product rule:

log5 ((7x + 4) / (2x – 1)) = 1

Now, we'll convert the logarithmic equation into an exponential form:

5^1 = (7x + 4) / (2x – 1)

5 = (7x + 4) / (2x – 1)

Multiplying both sides by (2x – 1) to eliminate the denominator:

5(2x – 1) = 7x + 4

10x - 5 = 7x + 4

Rearranging the terms:

10x - 7x = 4 + 5

3x = 9

Dividing by 3:

x = 3

So, the solution to the equation is x = 3.