Basic Mathematics & Logarithm
Properties of Logarithms
Grade 11
Question:
<p>If \(\log_a x = b\) for permissible values of <i>a</i> and <i>x</i>, then identify the statement(s) which can be correct:</p>
<p>(a) If <i>a</i> and <i>b</i> are two irrational numbers then <i>x</i> can be rational.</p>
<p>(b) If <i>a</i> rational and <i>b</i> irrational then <i>x</i> can be rational.</p>
<p>(c) If <i>a</i> irrational and <i>b</i> rational then <i>x</i> can be rational.</p>
<p>(d) If <i>a</i> rational and <i>b</i> rational then <i>x</i> can be rational.</p>
Step-by-Step Solution
Key Concept: Understand the relationship between the base, exponent, and result in the equation $a^b = x$ and when each can be rational or irrational
<p>Not provided in source material.</p>
Correct Answer: a, b, c, d