# Help find derivative of y with respect to variable

• Apr 5th 2010, 04:42 AM
KarlosK
Help find derivative of y with respect to variable
I have a problem which says

Y= 3^log(base2)t

I set it up as

ln y = log(base2)t (ln 3)

I am not sure what to do after this step!
• Apr 5th 2010, 04:50 AM
Jester
Quote:

Originally Posted by KarlosK
I have a problem which says

Y= 3^log(base2)t

I set it up as

ln y = log(base2)t (ln 3)

I am not sure what to do after this step!

Use the identity $\log_a x = \frac{\ln x}{\ln a}$.
• Apr 5th 2010, 04:50 AM
e^(i*pi)
Quote:

Originally Posted by KarlosK
I have a problem which says

Y= 3^log(base2)t

I set it up as

ln y = log(base2)t (ln 3)

I am not sure what to do after this step!

$\ln y = \log_2 (t) \cdot \ln(3)$

You can differentiate implictly given that $\frac{d}{dx} \ln (y) = \frac{1}{y} \cdot \frac{dy}{dx}$

You will also need to use the change of base rule on $\log_2 (t)$