# Thread: Convertion/translation of two equations

1. ## Convertion/translation of two equations

I have two tasks that I'm unable to work out, and I hope someone could help me :)

There are three unknown exponential functions:
y1 = f1 (t);
y2 = f2 (t);
y3 = f3 (t):

By measuring the values of t and yi, you get a linear relation between:

Yi = logci (yi) (log to the base of ci)
and t:
Yi = logsi (yi) = Ait + Bi (log to the base of si)

Describe the function f1 in the following way:
y1 = f1 (t) = Ce^(lambda*t)

The values are
i 1 2 3
Ai -1.25 1.53 -1.95
Bi 1.19 1.1 1.95
si 3.76 0.32 0.3

(i is always the base of A, B, s, Y and y)

Translate the equation
ln (y) = a ln (x) + b

to

y = f (x) = cx^r

when a=1.5486 b=0.9309

2. ## Re: Convertion/translation of two equations

I'm a little confused about si and ci in Task 1. If $\log{y} = Ax + B$, then you take $e$ to both sides to get $y=e^{Ax+B}=Ce^{Ax}$ where $C=e^B$.

It looks like Task 2 is a similar idea with $\log{x}$ instead of $x$:
$\log{y} = A \log{x} + B$
$e^{\log{y}} = e^{A \log{x} + B}$
$y = e^{A \log{x}}e^B$, and setting $C=e^B$ as before,
$y = Cx^A$
The identity $x^A=e^{A \log{x}}$ follows from the power rule for logarithms.

- Hollywood

3. ## Re: Convertion/translation of two equations

Thanks for the assistance! I managed to work it out by plotting in the values and using some of what you wrote

Cheers!