Given that the function $f$ is defined as $f:x\mapsto 1+{\log }_2\left(x-3\right)$ for $x\in \mathrm{ℝ}, x>3$, find an expression for $f^{-1}\left(x\right)$.

Solve.

${\log }_2\left({\log }_{3}x\right)=-1$

Solve.

${\log }_4{2}^{3-5x}=x^2$

$\begin{array}{lllllll}\boxed{{\log }_{3}9}& \boxed{{\log }_{2}8}& \boxed{{\log }_{3}20}& \boxed{{\log }_{3}4}& \boxed{{\log }_{2}2}& \boxed{{\log }_{4}3}& \boxed{{\log }_{2}3}\end{array}$

Without using a calculator, arrange these logarithms in ascending order.

Add some more logarithms of your own in the correct position in your ordered list. Use ${\log }_{e}2=0.693147,$ and ${\log }_{e}3=1.098612$, ${\log }_{e}5=0.6989$

Write as a single logarithm.

${\log }_{2}7+{\log }_{2}11$

Write as a single logarithm.

${\log }_{6}20-{\log }_{6}4$

Write as a single logarithm.

$3{\log }_{5}2-{\log }_{5}4$

Write as a single logarithm.

$2{\log }_{3}8-5{\log }_{3}2$

Write as a single logarithm.

$1+2{\log }_{2}3$