π > e
logπ > loge
log(logπ) > log(loge)
log(logπ)+logπ+loge > log(loge)+logπ+loge
log(π*e*logπ) > log(π*e*loge)
log(e*log(π^π)) > log(π*log(e^e))
log(log(π^π^e)) > log(log(e^e^π))
log(π^π^e) > log(e^e^π)
π^π^e > e^e^π

こんな感じ