Consider the exponential function y=b^x, b0. Determine the value for b for which the graph of y=b^x intersects the line y=x.

Question

Consider the exponential function y=b^x, b>0. Determine the value for b for which the graph of y=b^x intersects the line y=x.

aum · Answer

y = b^x
y = x
If the graphs intersect then b^x = x
Solve for x.

aum · Answer

I meant solve for b.

myininaya · Answer

The only way I can see how to solve for b such that b^x=x is to do it just by guessing...
There is one value b such that b^x=x from what I can tell.

myininaya · Answer

And I mean there is one value b such that b^x=x for some real value x

anonymous · Answer

what does it  mean that it must intersect the line y=x?

myininaya · Answer

that one curve must go through the other curve is what intersects means

myininaya · Answer

you have heard of intersections in highways

myininaya · Answer

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look at that exponential equation 
it doesn't touch the y=x line

myininaya · Answer

There should be a b that you can think of so that y=b^x is not an exponential equation

aum · Answer

It will if 0 < b < 1

aum · Answer

exponential decay function instead of a growth function.

aum · Answer

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