X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: f996b,6812b58dfe61342e X-Google-Attributes: gidf996b,public X-Google-ArrivalTime: 2001-11-21 08:54:01 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!newshub2.home.com!news.home.com!news1.sttln1.wa.home.com.POSTED!not-for-mail Message-ID: <3BFBDDB9.7020105@nowhere.com> From: Chess Player User-Agent: Mozilla/5.0 (Windows; U; Win98; en-US; rv:0.9.4) Gecko/20011019 Netscape6/6.2 X-Accept-Language: en-us MIME-Version: 1.0 Newsgroups: alt.ascii-art Subject: Re:Spoiler -- How can I solve this @#%#@%^#@$&^%*$%#@@#! References: <3bf81b34$0$9953$626a54ce@news.free.fr> Content-Type: multipart/related; boundary="------------070203020508010001040408" Lines: 94 Date: Wed, 21 Nov 2001 16:54:00 GMT NNTP-Posting-Host: 65.4.200.178 X-Complaints-To: abuse@home.net X-Trace: news1.sttln1.wa.home.com 1006361640 65.4.200.178 (Wed, 21 Nov 2001 08:54:00 PST) NNTP-Posting-Date: Wed, 21 Nov 2001 08:54:00 PST Organization: Excite@Home - The Leader in Broadband http://home.com/faster Xref: archiver1.google.com alt.ascii-art:11258 --------------070203020508010001040408 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit Well the answer is three, but you probably knew that. since 3^3 = 3*3*3 = 9 * 3. So what other numerical methods are there to solve this equation in the general sense. Graphically we could plot the curves y = 9x and y = 3^x and view thier intersecion. Which happens at x=3. (is this a request for ascii art?) Mathematically: We could treat it in a similar fashon to sloving high orer polynomials: Rewrite as 9x - 3^x = 0. Pick a number that is above the solution, such as four, try it, If it's too high, divide by two and subtract half then repeat until the answer is found. This suggests some calculus that I've fogotten. We could also rewrite as 3^2 * x = 3^x = 3^2*3^(x-2) and derive the simpler form x = 3 ^ (x-2) Then ln(x) = ln (3^x-2) Which is: ln(x) = x-2 * ln(3) finally ln(x)/x-2 = ln (3) Oh blast, where is my diff. eq. book Based upon the form of this equation, you have a method to determine if a solution exists and a method to solve it. Caution, you can't solve all equations. For instance 6x = 3^x has no real solution, just as 9(x+1) = 9x has no solution. I've gotten a bit off topic, didn't generate any ASCII art, only requested. Sorry in advance. Bruce Peterson --- BPeterson on www.chessclub.com - Channel 86 is the acsii art channel! My end-of-game greeting: ________ _____ _ ____ ______ __ __ ________ _______ _____ ___ _ __ _____ /_ __/ / / / | / | / / /_/ / __/ / /_/ / /_ __/ / / / ___/ / ___/ / | / | / | / ___/ / / / /_/ / /| |/ |/ / _/\__ \/___ / / / / /_/ / __/ / / ___/ /| |/ |/ | / __/ / / / __ / ___ | /| / /| | __/ / / / / / / __ / /__ / /__\ / ___ | /| / |/ /__ /_/ /_/ /_/_/ /_|/ |_/_/ |_| /___/ /_/ /_/ /_/ /_/____/ \_____/_/ /_|/ |_/|_|____/ Sebastian Pena wrote: >I've been working in this equation for years!!!!!!!!!! >Haven't found the way to solve it, maybe it's the wrong group though. >BTW, I'll send the last set of Hiragana tomorrow....... I'm feeling lazy. > > ## ## > ## ## > ### > ## ## > ####### ## ## ####### ## ## > ## ## ## ## ## ## > ## ## ## ## ##### ## > ######## ### ####### > ## ## ## ##### ## > ## ## ## ## ## ## > ####### ## ## ####### > >-- >/sps .|. > (*.*) > - > > -- The Portland Chess Club 8205 SW 25th Ave Portland, OR 97219 503-246-2978 Click to subscribe to pdxchess --------------070203020508010001040408--