examday

/TMUA

For a given value of $a$, let $f(x)=x^{(x+a)^{(x+2a)^{(x+3a)^{\cdots}}}}$. What is the value of $f(0.3)$ when $a=0.2$?

Note: $a^{b^{c^d}}=a^{\left(b^{(c^d)}\right)}$, i.e. power towers are evaluated from the top to the bottom.