# Transforming Logs.

• Jul 27th 2010, 06:45 PM
ASD2010
Transforming Logs.

What kind of transformation is represented by
log base b of x ----> log base (1/b) of x?

• Jul 27th 2010, 06:48 PM
pickslides
I would try some values for $x$ and $b$ and find the difference in their shapes.
• Jul 27th 2010, 08:43 PM
ASD2010
Thank You, That really helps :)
• Jul 27th 2010, 10:49 PM
yehoram
Logs
$log_bx = a \ \ \ \ \ \ \ b^a = x \ \ \ \ \ \ \ \ \ \ \ \\ log_{\frac{1}{b}}x = a \ \ \ \ \ \ \ \ \ (\frac{1}{b})^a = x \ \ \ \ \ \$

Have a good day from Israel !(Hi)
• Jul 27th 2010, 10:58 PM
ASD2010
Sice the question is asking for teh type of transformation, would it be wrong if i answered , The transformation is reflected on the x-axis. Meaning the y-values are negative.!

Thank You for your help :)
• Jul 28th 2010, 02:04 AM
mr fantastic
Quote:

Originally Posted by ASD2010
Sice the question is asking for teh type of transformation, would it be wrong if i answered , The transformation is reflected on the x-axis. Meaning the y-values are negative.!

Thank You for your help :)

I would answer in the following way: $\displaystyle \log_{\frac{1}{b}} (x) = - \log_b (x)$ therefore the transformation is reflection in the x-axis.
• Jul 28th 2010, 03:52 AM
HallsofIvy
More specifically, $log_{\frac{1}{b}}(x)= \frac{log(x)}{log(\frac{1}{b})}= \frac{log(x)}{- log(b)}$ $= -\frac{log(x)}{log(b)}= -log_{b}(x)$