SOLUTION: Mr. Jellyby was working with transformations of exponential functions when he believed he made a discovery. He found out thatall exponential functions b^x could be written as e^nx,

Algebra ->  Functions -> SOLUTION: Mr. Jellyby was working with transformations of exponential functions when he believed he made a discovery. He found out thatall exponential functions b^x could be written as e^nx,      Log On


   

Question 591535: Mr. Jellyby was working with transformations of exponential functions when he believed he made a discovery. He found out thatall exponential functions b^x could be written as e^nx, where the value of n dependedon the value of b.
a. For b=2, slove for n ( that is, solve for n in the equation 2^x=e^nx.)
b Write a formula to determine n given any b.
Found 2 solutions by ankor@dixie-net.com, richard1234:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a. For b=2, solve for n ( that is, solve for n in the equation 2^x=e^nx.)
2%5Ex+=+e%5E%28nx%29
ln%282%5Ex%29+=+ln%28e%5E%28nx%29%29
log equiv of exponents, ln(e) = 1
x*ln(2) = nx
divide both side by x
ln(2) = n
n = .693
:
b Write a formula to determine n given any b.
n = ln(b)

Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do part b) first, then you can use the result to do part a) easily.

We have



We can write the RHS as , in other words,