The monotone increasing interval of function f (x) = log5 (2x + 1) is______ ．

The monotone increasing interval of function f (x) = log5 (2x + 1) is______ ．

In order to make the analysis of function meaningful, then 2x + 1 > 0, so the domain of definition of function is (- 12, + ∞). Because the inner function u = 2x + 1 is an increasing function and the outer function y = log5u is also an increasing function, the function f (x) = log5 (2x + 1) increases monotonically in the interval (- 12, + ∞), so the monotonic increasing interval of function f (x) = log5 (2x + 1) is (- 12, + ∞), so the answer is: (- 12, + ∞)