To solve the inequality log7 (x-1) ≤ log7 2 + log7 3, we can use the properties of logarithms.

First, we can combine the logarithms on the right side of the inequality:

log7 2 + log7 3 = log7 (2*3) = log7 6

So the inequality becomes:

log7 (x-1) ≤ log7 6

Next, we can remove the logarithms by converting them to exponential form:

7^(log7 (x-1)) ≤ 7^(log7 6)

This simplifies to:

x-1 ≤ 6

Now we can solve for x:

x ≤ 7

Therefore, the solution to the inequality log7 (x-1) ≤ log7 2 + log7 3 is x ≤ 7.