(Solved): (Figure 1) shows a graph of \( \log T \) versus \( \log r \) for the planctary data. Consider two ...

(Figure 1) shows a graph of \( \log T \) versus \( \log r \) for the planctary data. 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 Such a graph is called a fog-tog greph. The scales in the figure are \( x=\log u \) and \( y=\log v \). Find an expression for \( y \) in terms of \( x \). logar ithmic, not linear, meaning that each division along the axis Express your answer in terms of the variables \( q, p, C \) and \( x \). corresponds to a factor of 10 increase in the value. Strictly speaking. the "correct' labels on the \( y \) - - \( x \times 15 \) should be \( 7,8,9 \), and 10 because liese are the logarithens of \( 10^{7}, \ldots, 10^{111} \). Figure Part B Use the experimentally determined "best fit" line to tind the mass of the sun. What shape will a graph of \( y \) versus \( x \) have?