.

Show which of the following quantities is larger:

$\displaystyle log_2{3} \ \ or \ \ log_3{5}$

Demonstrate it. You may not use a calculator, computer, or logarithm tables.

You may not use calculus, in the sense that you may not use derivatives or antiderivatives.

You may use arithmetic and high school algebra to include the rules of exponents and logarithms.