Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 18: Mixed practice

Rewrite in terms of $\log a,\log b,$ and $\log c$:

$\log \left(abc\right)$

Rewrite in terms of $\log a,\log b,$ and $\log c$:

$\log \left(\frac{ac}{b}\right)$

Rewrite in terms of $\log a,\log b,$ and $\log c$:

$\log \left(a^3{b}^2{c}^4\right)$

Rewrite in terms of $\log a,\log b,$ and $\log c$:

$\log \left(a\sqrt{b}\right)$

Rewrite in terms of $\log a,\log b,$ and $\log c$:

$\log \left(a\sqrt{\frac{b}{c^2}}\right)$

Use properties of logarithms to find an equivalent expression for the given function. Then describe the sequence of transformations on the graph of $y={\log }_{3}x$ that give the graphs of the equivalent expressions for $f$.

$f\left(x\right)={\log }_3\left(27x\right)$

Use properties of logarithms to find an equivalent expression for the given function. Then describe the sequence of transformations on the graph of $f\left(x\right)={\log }_{3}x$ that give the graphs of the equivalent expressions for $g$.

$g\left(x\right)={\log }_3(x-9{)}^4$

Solve the following logarithmic equation

$\log (x-5)-\log (x+4)=-1$