LOGS

**bigton** · November 4th 2008, 05:08 PM

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

**bigton** · November 4th 2008, 06:01 PM

Which rule would you use first

**bigton** · November 4th 2008, 06:23 PM

the problem is f(x) = 2^(log(3) x)
sorry about that

**akolman** · November 4th 2008, 06:39 PM

So you have something like this

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

$\log {y}=\log {(2^{(\log {3})x})}=(\log{2})(\log {3})x$
Now differentiate both sides
$\frac{1}{y} y'=(\log{2})(\log {3})$
$y'=(\log{2})(\log {3})y=(\log{2})(\log {3})2^{(\log {3})x}$

**Soroban** · November 4th 2008, 06:53 PM

Hello, bigton!

We're expected to know these two formulas:

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

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

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

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

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