Logarithmic Differentation

**cjmac87** · October 3rd 2008, 03:25 PM

Any help with solving this... I can't figure it out.

$3^xlog_8(x)$

That is, I need to find the derivative. I think this is the first step:

$ln(3)/ln(8)$

**icemanfan** · October 3rd 2008, 03:33 PM

$3^x \log_8 x = \frac{3^x \ln x}{\ln 8}$

**cjmac87** · October 3rd 2008, 03:49 PM

Do i continue with using the quetient rule. Is f'(x)= $3^xln(x)*3$ ?

**skeeter** · October 3rd 2008, 04:51 PM

Originally Posted by cjmac87

Do i continue with using the quetient rule. Is f'(x)= $3^xln(x)*3$ ?

$\frac{3^x \ln{x}}{\ln{8}} = \frac{1}{\ln{8}} \cdot 3^x \ln{x}<br />$

use the product rule ...

$\frac{1}{\ln{8}}\left(3^x \cdot \frac{1}{x} + 3^x \cdot \ln{3} \cdot \ln{x}\right)$

now clean up the algebra.

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