# Probability density function for a logarithmic spinner [duplicate]

I'm having trouble deriving the PDF for the following problem (from the book Doing Bayesian analysis with R and BUGS):

Consider a spinner of the kind often found with board games, but with a log10 scale from 1 to 100 (covering 0 to 360 deg). The spinner is fair, so any value is equally likely. What is the pdf at point $x$?

I know that the $x$ value at angle $t$ is given by

$$x = 100^\text{t/360}$$

Doing some transformation

$$x = \exp^{(t/360) \times \log(100)}$$

$$pdf(x) = pm(x)/dx$$

I also know

$$dt/dx = 360/(\log100 \times x)$$

## Question

How to derive the answer below, using the information above?

$$pdf(x) = 1/(2 \times ln(10) \times x)$$

Thanks.

## marked as duplicate by whuber♦Oct 7 '13 at 14:07

• Fernando, please add the self-study tag to the question. – COOLSerdash Oct 7 '13 at 15:02