Re: Find a in the y=a^x graph!
- From: "Narasimham" <mathma18@xxxxxxxxxxx>
- Date: 16 Nov 2006 00:17:50 -0800
131208@xxxxxxxxx wrote:
Narasimham 작성:
131208@xxxxxxxxx wrote:
There is a picture of an exponential graph in the plane.
We know that this graph is of the form y=m^x.
But we don't have any other information about this graph.
Axes are not drawed.
We have a ruler and a compass.
Can we find "m" of y=m^x?
m is 'x' th root of y. Even a cube root y cannot be found with ruler
and compass.Why not use a calculator ?
x and y are variables. I meant f(x) = m^x which is an exponential
function.
And my question is about "can we find a base "m" of f(x) = m^x when we
see just a picture of some exponential function" using a ruler and a
compass.
Your question has still left out a small vague area.Please attach a
link to graph of the "some exponential function " that you have more
clearly in your mind.The graph would give the available 1 unit as grid
marking or as initial y intercept, whether the exp/log curve is rotated
in x- y plane or whether x-, y-, axes are erased along with grid and so
on.
Since dy/dx = y*log(m) you can pull a constant out of its differentials
and slope at any point.
In particular, the sub-tangent of an exponential curve y = m^x is
constant and equals 1/log(m) at any point,by drawing tangent ant line
parallel to x-axis provided it is also given,can be measured and m
computed,but still not possible by ruler and compass.This is 1 for the
particular case y = e^x.
You could also post to geometry.puzzles
.
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