Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Equivalent Quantities: Exponentials and Logarithms, Exercise 30: Exercise 9I

If $m={\log }_{5}7$ and $n={\log }_{5}4$, write the expression in terms of $m$ and $n$ :

$\frac{{\log }_{5}7}{{\log }_{5}4}$

If $m={\log }_{5}7$ and $n={\log }_{5}4$ and if  $\frac{{\log }_{5}49}{{\log }_{5}64}=\frac{pm}{qn}$, then find $p+q$.

If $m={\log }_{5}7$ and $n={\log }_{5}4$, write the expression in terms of $m$ and $n$ :

${\log }_{5}100$

Let $x={\log }_{2}A,y={\log }_{2}B$ and $z={\log }_{2}C$. Express ${\log }_2{\left(\frac{A}{B{C}^3}\right)}^4$ in terms of $x,y,z$.

If ${\log }_{3}P=x$ and ${\log }_{3}Q=y$, write the expression in terms of $x$ and $y$ :

${\log }_3{P}^{3}Q$

If ${\log }_{3}P=x$ and ${\log }_{3}Q=y$, write the expression in terms of $x$ and $y$ :

${\log }_3\frac{\sqrt{P}}{Q}$

Given that $\log x-\log (x-5)=\log M$, express $M$ in terms of $x$.

Solve the equation $\log x-\log (x-5)=1$ to find the value of $x$.