Logarithms

Laws of logarithms

Complete Code

PG problem file

Explanation

DOCUMENT();

loadMacros('PGstandard.pl', 'PGML.pl', 'PGcourse.pl');

Preamble

These standard macros need to be loaded.

Context()->variables->are(x => 'Real', y => 'Real', z => 'Real');
Context()->variables->set(x => { limits => [ 2, 3 ] });
Context()->variables->set(y => { limits => [ 2, 3 ] });
Context()->variables->set(z => { limits => [ 2, 3 ] });

$a = random(20, 40);
$b = random(20, 40);
do { $c = random(20, 40); } until ($c != $b);

# TeX
$expr =
    "\displaystyle \ln \left( \frac{ x^{$a} y^{$b} }{ z^{$c} } \right)";

$answer = Compute("$a * ln(x) + $b * ln(y) - $c * ln(z)");

Context()->operators->undefine('/', '^', '**');
Context()->functions->undefine('sqrt');

Setup

We add the variables to the context and reset their limits since logarithms are not defined on the default domain [-1,1]. After defining $answer, then we undefine certain operators and functions so that students will have to simplify their answer. Since the answer requires multiplication no matter how it is written, we cannot prevent students from entering an answer such as ln(x*x*x...) instead of $a * ln(x), but by choosing large values for $a, $b, $c, we can strongly discourage them from entering ln(x*x*x...).

BEGIN_PGML
Using laws of logarithms, write the expression below using sums and/or
differences of logarithmic expressions which do not contain the logarithms of
products, quotients, or powers.

[`\displaystyle [$expr] =`] [_]{$answer}{20}
END_PGML

Statement

This is the problem statement in PGML.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.