# Thread: How to combine two logarithmic equations?

1. ## How to combine two logarithmic equations?

The following curves have been separately drawn by the function
$$y=m-ln(t^{-1/2}-n)$$
$n$ is the same in both curves ($0.1$), $m$ is $0$ in the orange and $11$ in the blue.

Is it possible to write a single equation to draw both curves continuously? Note that the blue curve has been shifted (+100) to show what I want.

2. ## Re: How to combine two logarithmic equations?

it's cheating a bit using the floor function but here you go.

$y(t) = 11 \left \lfloor \dfrac {t}{100}\right\rfloor - \ln\left(\left(t - 100 \left\lfloor \dfrac{t}{100}\right \rfloor \right)^{-1/2}-0.1\right)$

3. ## Re: How to combine two logarithmic equations?

Originally Posted by romsek
it's cheating a bit using the floor function but here you go.

$y(t) = 11 \left \lfloor \dfrac {t}{100}\right\rfloor - \ln\left(\left(t - 100 \left\lfloor \dfrac{t}{100}\right \rfloor \right)^{-1/2}-0.1\right)$
Are you sure it works? I get this curve instead

4. ## Re: How to combine two logarithmic equations?

Originally Posted by brianx
Are you sure it works? I get this curve instead