Question 8:
A simple Google search for "log properties" yields Logarithmic Properties -- LEARN ALL OF THESE!
These properties must be understood to solve this problem:
1) $\displaystyle \log_b(xy) = \log_b(x) + \log_b(y)$
2) $\displaystyle \log_b(\tfrac{x}{y}) = \log_b(x) - \log_b(y)$
3) $\displaystyle \log_b(x^n) = n\log_b(x)$
First, change $\displaystyle \displaystyle^8\sqrt{7}$ to $\displaystyle 7^{\tfrac{1}{8}}$, which I explained earlier.
$\displaystyle \small{\log_{15}\frac{7^{\frac{1}{8}}}{y^2x} = \color{red}\log_{15}(7^{\frac{1}{8}}) \color{black} - \color{blue}\log_{15}(y^2x)\color{black} = \color{red}\frac{1}{8}\log_{15}(7)\color{black} - \color{blue} \left(\underbrace{\log_{15}(y^2)}_{\text{Same as }2\log_{15}(y)} + \log_{15}(x) \right) \color{black}= \tfrac{1}{8}\log_{15}(7) - 2\log_{15}(y) - \log_{15}(x)}$