20071206, 08:16  #1 
Nov 2005
2×7×13 Posts 
2^x using powers of e?
I have an equation like: 2^(xa)=e^x, where a=1/ln (2)
I wonder how I'd go about finding an equation that gives me a power of 2 without using 2^x. In other words, f(g(h(...(x)...))) gives 2^x where it is prefered for f,g,h... to all be in terms of logarithms and powers of e. I could swear this is a simple matter but I just can't seem to find the correct function. I've been trying to apply the rules I learned in college algerbra a few years ago and can't get it to work. Has anyone got an answer or method to arrive at one? Thanks, Joe 
20071206, 10:17  #2 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}·13·127 Posts 
What is wrong with: e^(x*ln(2))=2^x

20071206, 12:48  #3 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2^{4}×719 Posts 

20071206, 13:36  #4  
"Bob Silverman"
Nov 2003
North of Boston
2×3×29×43 Posts 
Quote:
illustrates some of the serious problems we have today in mathematics education. Normally, logarithms are a second year algebra topic for junior high school (if one isn't clueless), or high school (if one is clueless). I say this because people who are not clueless generally start taking algebra BEFORE high school. 

20071206, 15:17  #5  
"Lucan"
Dec 2006
England
14512_{8} Posts 
Quote:
How about you? David 

20071206, 15:28  #6 
Jun 2003
The Texas Hill Country
3^{2}×11^{2} Posts 
Bob,
In defense of Joe, in my math education, I covered many topics at least three or four times. What we covered at the graduate level encompassed, and extended what we had covered at the undergraduate level. Similarly, the college level included that which was previously covered in high school. That is not to imply that in the later courses we spent much, if any, time on "how", but probably derived the "why" of a procedure that we learned earlier. But, if you can really pinpoint just where in your education you first learned each topic, then I fear that you are placing more emphasis on the "educational curriculum" rather than on the "math" itself. For example, when are the concepts of "set theory" taught? So, specifically to Joe's remark, I interpret it to be inclusive of "College Algebra" rather than limited to just the additional concepts introduced at that level. 
20071206, 15:42  #7  
"Bob Silverman"
Nov 2003
North of Boston
2·3·29·43 Posts 
Quote:
And it isn't just in mathematics. My kids attend the SAME high school that I did. When I compare what I was taught with what they are being taught, I get disgusted. Ask the average U.S. high school student today: Define "dangling particple". What is "faulty parallel sentence construction" Where is Ulan Bator located? What about Madagascar? (etc.) What conflict did Andrew Jackson have with the Supreme Court? How did he violate the Constitution? What is electronegativity? Why is it higher for Cesium than Potassium? What is the electronic configuration for Carbon? What are Kepler's Three laws? If and object with mass M1 and momentum P1 collides inelastically with an object of mass M2 and momenturn P2 at angle theta, describe the vectors of the two objects after collision. Who said "that which we call a rose, by any other name would smell as sweet"? etc. etc. etc. Kids today are lazy, ignorant, and don't care about educating themselves. Even my old teachers say the same thing. My generation was much more educationally motivated than today's generation. And what I see in this forum is people who just want to run other people's code without bothering to learn about how/why it works. They want to pretend they are accomplishing something by factoring numbers that noone else cares about using code written by others and about which they are totally ignorant. They want rewards and recognition without being willing to put in the work. I recall Debbie Allen's (from Fame) comments: "You want fame? Well fame COSTS." The wannabees have the right to do what they want. It is their machines and their time. And I have the right to be contemptuous. 

20071206, 15:50  #8  
"Lucan"
Dec 2006
England
2·3·13·83 Posts 
Quote:
Pink Floyd (We don't need no educashion) Or was I thinking of "Schools Out":) Last fiddled with by davieddy on 20071206 at 15:53 

20071206, 16:44  #9 
∂^{2}ω=0
Sep 2002
Repรบblica de California
2DE1_{16} Posts 
Back in my wildncrazy college days, I almost got arrested for waving my dangling participle at someone. Bob is 100% correct  If I'd been properly taught about that concept in HS, my subsequent legal neardiscomfiture could have been avoided.

20071206, 18:18  #10  
Feb 2007
2^{4}×3^{3} Posts 
back to the topic...
Quote:
(independently of how you define +1...) So another simple solution might be (6/3)^x. Or, exp(ln(6)/ln(3)). Or exp(ln(6^(1/ln(3)))) well I just notice: "... a power of 2"  does this mean "any" ? Then 1 is the most simple answer. Or 4, if "positive" is tacitely understood. did I miss something or was there some comment on the first (ontopic) proposals ? PS: I agree on deficiencies / degradation of the teaching system, but IMHO this has nothing to do with the average IQ of the kids. http://en.wikipedia.org/wiki/Cui_bono ? This is a purely political (I'd even be enclined to say economical) choice. For politics and economy, it is much better to have stupid consumers. PPS: and it is quite hard for parents to struggle against the overwhelming influence of that allencompassing "institution". Probably the absence of a TV set at home would make things easier. Well, starting to struggle already means that parents themselves are not yet brainwashed. Gets rare, that species... Last fiddled with by m_f_h on 20071206 at 18:26 

20071206, 18:36  #11  
"Bob Silverman"
Nov 2003
North of Boston
2·3·29·43 Posts 
Quote:
about the dumbing down of America. When I was in high school, being selected into the National Honor Society was (somewhat of) an honor. From my class of 430, we had about 35 students selected. It was considered the equivalent of Phi Beta Kappa for high school. My daughter was just inducted. Now, it is no longer considered the equivalent to Phi Beta Kappa. To join, one is also selected for "leadership, and "performing community service". Indeed, one needs to get documents signed showing that one has performed some minimal number of hours of community service. Not only that, but the academic requirements have been watered down. To qualify, one needs an overall overage of 98/100 where the average is computed by giving a 20% extra weight to any honors course and a 15% weight to the level of courses just below honors level. YECH!!!! Some 122 students in my daughter's class were elected. This is about 28% of her class. WHAT A JOKE!!!! This "honor society" has become about as exclusive as a rainstorm. The "honor" has been so totally diluted as to be almost meaningless. If one also looks at the "academic honor roll" for the high school that is printed in the local paper, and compares the number of students getting "high honors" vs. my high school class, it is 3 to 4 times as many students. So grade inflation has struck as well. Now, if students were actually getting smarter, or learning more, this could all be justified. I note, however, that the number of National Merit scholars has actually DECLINED since I went to high school. My class had 8 finalists and some 19 honorable mentions. (Last year's class only had 3 finalist and half the number of honorable mentions) (For nonU.S. people, the National Merit Scholarships are awarded as the result of a competitive test in Math & English. They are the preliminary SAT tests) It is all part of the dumbing down of America. 

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