FIGURE 13.17 showed a graph of log T versus log r for the

QUESTION:

Figure  showed a graph of \(\log T\) versus \(\log r\) for the planetary data given in Table 13.2. Such a graph is called a loglog graph. The scales in Figure  are logarithmic, not linear, meaning that each division along the axis corresponds to a factor of 10 increase in the value. Strictly speaking, the "correct" labels on the \(y\) -axis should be \(7,8,9\), and 10 because these are the logarithms of \(10^{7}, \ldots, 10^{10}\).
a. Consider two quantities \(u\) and \(v\) that are related by the expression \(v^{p}=C u^{q}\), where \(C\) is a constant. The exponents \(p\) and \(q\)are not necessarily integers. Define \(x=\log u\) and \(y=\log y\).. Find an expression for \(y\) in terms of \(x\).
b. What shape will a graph of \(y\) versus \(x\) have? Explain.
c. What slope will a graph of \(y\) versus \(x\) have? Explain.
d. Use the experimentally determined "best-fit" line in Figure  to find the mass of the sun.

Equation Transcription:

Text Transcription:

logT

logr

y

7,8,9

10^7 ,..., 10^10

u

v

v^p = Cu^q

C

p

q

x=logu

y=logv

y

x

y

x

y

x