Maximum Problem

[lrdheat]

I’m wondering if solve app can be used to determine the value of x that is a maximum in producing a value of 1 for the integral from 0 to x of a^X. It appears as if a^~1.72 is the maximum. Integral from 0 to x of a^3 reaches 1 at ~1.414 (sqrt 2). Using a^1.72, the integral totals 1 when x reaches ~1.4447. Using a^1 the integral reaches 1 when x once again reaches ~1.414 (sqrt 2).

If not achievable in solve, how might I approach this problem? (Not for any purpose, just found myself curious when figuring out how to use the solve app with integrals!)