Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Equivalent Quantities: Exponentials and Logarithms, Exercise 34: Exercise 9K

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{6}3$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{3}36$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{3}54$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{9}6$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{6}18$

If ${\log }_{x}3=r$ and ${\log }_{x}6=s$, write the given expression in terms of $r$ and $s$:

${\log }_{3}2$

Prove that ${\log }_{x}y=\frac{1}{{\log }_{y}x}$

Show that $\ln 10=\frac{1}{\log e}$