Basic Mathematics & Logarithm
Properties of Logarithms
Grade 11
Question:
<p>From the relation <span class="latex">r^q = p^r</span> derived from <span class="latex">x = r^q</span> and <span class="latex">x = p^r</span>, find the value of <span class="latex">p</span>.</p>
<p>(a) <span class="latex">r^q</span></p>
<p>(b) <span class="latex">r^{q/r}</span></p>
<p>(c) 1</p>
<p>(d) <span class="latex">r^r</span></p>
Step-by-Step Solution
Key Concept: Apply logarithmic manipulation to the equation <span class="latex">r^q = p^r</span> by taking logarithms of both sides.
<p><strong>Step 1:</strong> From the relation <span class="latex">r^q = p^r</span>, take logarithm of both sides: <span class="latex">q \log r = r \log p</span></p><p><strong>Step 2:</strong> Rearranging: <span class="latex">\log p = \frac{q \log r}{r}</span></p><p><strong>Step 3:</strong> Therefore: <span class="latex">p = r^{q/r}</span></p><p>∴ Answer is (a) <span class="latex">r^q</span></p>
Correct Answer: A