To solve this logarithmic equation, we can use the property of logarithms that states if log_a(b) = log_a(c), then b = c.

Given:

log4(4+7x) = log4(1+5x) + 1

Using the property mentioned above, we get:

4+7x = 1+5x + 4

Now, we can simplify the equation:

7x - 5x = 1

2x = 1

x = 1/2

Therefore, the solution to the equation log4(4+7x) = log4(1+5x) + 1 is x = 1/2.