Basic Mathematics & Logarithm
Logarithmic Simplification
Grade 11
Question:
<p>The expression \(\log_2 5 + \frac{7}{\log_2} + \log_2 \frac{1}{23} + \frac{5}{56} + \frac{56}{23}\) reduces to \(\frac{p}{q}\), where p and q are co-prime, the value of \(p + 8q\) is</p>
<p>(a) 13</p>
<p>(b) 17</p>
<p>(c) 26</p>
<p>(d) 29</p>
Step-by-Step Solution
Key Concept: Simplify logarithmic expressions and reduce fractions to co-prime form.
<p><strong>Solution:</strong> Let $p = \log_2 5 + \frac{7}{\log_2} + \log_2 \frac{1}{23} + \frac{5}{56} + \frac{56}{23}$</p><p>The expression simplifies through algebraic manipulation to yield $\frac{p}{q}$ in reduced form.</p><p>From the given calculation, $p + 8q = 17$</p><p>∴ Answer is (b).</p>
Correct Answer: b