# LOGS

• Nov 4th 2008, 05:08 PM
bigton
LOGS
Find f'(x)
e) f(x) 2^(log(3)x)

The 3 is subscript

Guys this is the last problem for my homework help me through this
• Nov 4th 2008, 06:01 PM
bigton
Which rule would you use first
• Nov 4th 2008, 06:23 PM
bigton
the problem is f(x) = 2^(log(3) x)
• Nov 4th 2008, 06:39 PM
akolman
So you have something like this

$\displaystyle y=2^{(\log {3})x}$ and you want to find $\displaystyle y'$

$\displaystyle \log {y}=\log {(2^{(\log {3})x})}=(\log{2})(\log {3})x$
Now differentiate both sides
$\displaystyle \frac{1}{y} y'=(\log{2})(\log {3})$
$\displaystyle y'=(\log{2})(\log {3})y=(\log{2})(\log {3})2^{(\log {3})x}$
• Nov 4th 2008, 06:53 PM
Soroban
Hello, bigton!

We're expected to know these two formulas:

. . $\displaystyle f(x) \:=\:b^u \quad\Rightarrow\quad f'(x) \:=\:b^u\,u'\ln(b)$

. . $\displaystyle f(x) \:=\:\log_b(u) \quad\Rightarrow\quad f'(x) \:=\:\frac{1}{u\ln(b)}$

Quote:

Find $\displaystyle f'(x)\!:\;\;f(x) \:=\:2^{\log_3(x)}$

$\displaystyle f'(x) \;=\;2^{\log_3(x)}\cdot\frac{1}{x\ln(3)}\ln(2) \;=\;\frac{2^{\log_3(x)}\ln(2)}{x\ln(3)}$