To solve this logarithmic equation, we first need to use the properties of logarithms to simplify the expression.

Use the property: log_a(x) - log_a(y) = log_a(x/y)
log₁/₇(2x + 5) - log₁/₇(6) = log₁/₇(2)

Rewrite the expression using the property above:
log₁/₇((2x + 5)/6) = log₁/₇(2)

Since the bases of the logarithms are the same, we can drop the logarithms:
(2x + 5) / 6 = 2

Multiply both sides by 6 to get rid of the fraction:
2x + 5 = 12

Subtract 5 from both sides to isolate x:
2x = 7

Divide by 2 to solve for x:
x = 7/2

Therefore, the solution to the logarithmic equation log₁/₇(2x + 5) - log₁/₇(6) = log₁/₇(2) is x = 7/2.