people need to think with their heads. hear i explain what 2^x=10. you must not use log rithems to solve but you must use your mind. the answer is 3.625, and other people say its 3.321. my answer is right and 3.321 is wrong as i explain in this video.http://www.youtube.com/user/kirstybrewster copy and paste link thankyou
-
You say that 2*2*2*1.25 = 10, so
2^(2/2 + 2/2 + 2/2 + 1.25/2) = 10
I then say that 2*2*2.5 = 10, so
2^(2/2 + 2/2 + 2.5/2) = 10
But 2/2 + 2/2 + 2/2 + 1.25/2 = 3.625, while 2/2 + 2/2 + 2.5/2 = 3.25, which is not the same. Supposing your reasoning was correct, it yields nonsense. You could actually define exponentiation in such a way that your answer is correct, but that's not the usual definition, and it would lack most of the usual elegance--for instance, it would be discontinuous.
To be blunt, you're a mathematical crank in the making (see my reference for a description; I don't mean to insult you). I hope that you learn to see the error of your ways rather than being constantly disappointed by having nobody accept your ideas. Some cranks spend years of their life on impossible problems. That just doesn't seem like a life anyone would choose willingly.
On another note, I'm actually quite fine with strong reliance on calculators and, more generally, computer algebra systems. They're tools, like linear algebra is a tool. I don't see their negative effects. I wouldn't trust most people's hand-done arithmetic regardless, so I'm glad Excel or their calculator does it all for them. Also, almost nobody needs to know how various functions are actually evaluated. A friend of mine is an experimental chemist. If she had to learn an efficient series representation for, say, the Bessel functions, that would take time away from learning chemistry that might actually benefit someone.
2^(2/2 + 2/2 + 2/2 + 1.25/2) = 10
I then say that 2*2*2.5 = 10, so
2^(2/2 + 2/2 + 2.5/2) = 10
But 2/2 + 2/2 + 2/2 + 1.25/2 = 3.625, while 2/2 + 2/2 + 2.5/2 = 3.25, which is not the same. Supposing your reasoning was correct, it yields nonsense. You could actually define exponentiation in such a way that your answer is correct, but that's not the usual definition, and it would lack most of the usual elegance--for instance, it would be discontinuous.
To be blunt, you're a mathematical crank in the making (see my reference for a description; I don't mean to insult you). I hope that you learn to see the error of your ways rather than being constantly disappointed by having nobody accept your ideas. Some cranks spend years of their life on impossible problems. That just doesn't seem like a life anyone would choose willingly.
On another note, I'm actually quite fine with strong reliance on calculators and, more generally, computer algebra systems. They're tools, like linear algebra is a tool. I don't see their negative effects. I wouldn't trust most people's hand-done arithmetic regardless, so I'm glad Excel or their calculator does it all for them. Also, almost nobody needs to know how various functions are actually evaluated. A friend of mine is an experimental chemist. If she had to learn an efficient series representation for, say, the Bessel functions, that would take time away from learning chemistry that might actually benefit someone.
-
I agree that scientific/graphing calculators are used too much. I can personally find the value of any trigonometric, logarithmic, transcendental, exponential function or solution to any equation using only a +-*/ calculator by using knowledge of series, Newton's method, interpolation, and other common techniques. Sometimes I don't even need one. Besides how do you learn anything if you have a calculator doing it all for you?