May 18, 2018

Use properties of logarithms for all of the following.

i) ${\log}_{p} \sqrt{x} = {\log}_{p} {x}^{\frac{1}{2}} = \frac{1}{2} {\log}_{p} x = \frac{9}{2}$

ii) ${\log}_{p} \left(\frac{1}{x}\right) = {\log}_{p} 1 - {\log}_{p} x = 0 - 9 = - 9$

iii) ${\log}_{p} \left(x y\right) = {\log}_{p} x + {\log}_{p} y = 9 + 6 = 15$

iv) ${\log}_{y} x = \log \frac{x}{\log} y = {\log}_{p} \frac{x}{\log} _ p y = \frac{9}{6} = \frac{3}{2}$

Hopefully this helps!