Qualcuno mi aiuti:
<BR>per quli valori reali di x: a^x=x^2 ?
Aiuto
Moderatore: tutor
-
- Messaggi: 173
- Iscritto il: 01 gen 1970, 01:00
- Località: Piacenza
Eccone una calcolata dal mio computatore (scusate se non si capisce niente):
<BR>
<BR>\\!\\(Log[a] ≠ 0 && \\((\\[ExponentialE]\\^\\(\\(-2\\)/\\[ExponentialE]\\) ≤ a < 1 && \\
<BR>\\((x == \\(-\\(\\(2\\ ProductLog[Log[a]\\/2]\\)\\/Log[a]\\)\\) ||
<BR> x == \\(-\\(\\(2\\ ProductLog[\\(-1\\),
<BR> Log[a]\\/2]\\)\\/Log[a]\\)\\))\\) || a > 1 && x == \\(-\\(\\(2\\ \\
<BR>ProductLog[Log[a]\\/2]\\)\\/Log[a]\\)\\) || 0 <
<BR> a < 1 && x == \\(-\\(\\(2\\
<BR> ProductLog[\\(-\\(Log[a]\\/2\\)\\)]\\)\\/Log[
<BR> a]\\)\\) || 1 < a ≤ \\[ExponentialE]\\^\\(2/\\
<BR>\\[ExponentialE]\\) && \\((
<BR> x == \\(-\\(\\(2\\
<BR> ProductLog[\\(-\\(Log[
<BR> a]\\/2\\)\\)]\\)\\/Log[a]\\)\\) || x == \\(-\\(\\(2\\ ProductLog[\\(-1\\), \\
<BR>\\(-\\(Log[a]\\/2\\)\\)]\\)\\/Log[a]\\)\\))\\))\\)\\)
<BR>
<BR>\\!\\(Log[a] ≠ 0 && \\((\\[ExponentialE]\\^\\(\\(-2\\)/\\[ExponentialE]\\) ≤ a < 1 && \\
<BR>\\((x == \\(-\\(\\(2\\ ProductLog[Log[a]\\/2]\\)\\/Log[a]\\)\\) ||
<BR> x == \\(-\\(\\(2\\ ProductLog[\\(-1\\),
<BR> Log[a]\\/2]\\)\\/Log[a]\\)\\))\\) || a > 1 && x == \\(-\\(\\(2\\ \\
<BR>ProductLog[Log[a]\\/2]\\)\\/Log[a]\\)\\) || 0 <
<BR> a < 1 && x == \\(-\\(\\(2\\
<BR> ProductLog[\\(-\\(Log[a]\\/2\\)\\)]\\)\\/Log[
<BR> a]\\)\\) || 1 < a ≤ \\[ExponentialE]\\^\\(2/\\
<BR>\\[ExponentialE]\\) && \\((
<BR> x == \\(-\\(\\(2\\
<BR> ProductLog[\\(-\\(Log[
<BR> a]\\/2\\)\\)]\\)\\/Log[a]\\)\\) || x == \\(-\\(\\(2\\ ProductLog[\\(-1\\), \\
<BR>\\(-\\(Log[a]\\/2\\)\\)]\\)\\/Log[a]\\)\\))\\))\\)\\)
In the break of new dawn
My hope is forlorn
Shadows they will fade
But I'm always in the shade
Without you...
My Selene - Sonata Arctica
My hope is forlorn
Shadows they will fade
But I'm always in the shade
Without you...
My Selene - Sonata Arctica