Basic Mathematics & Logarithm
Logarithmic Inequalities
Grade 11
Question:
<p>If <i>a</i> = log₃ 5, <i>b</i> = log₁₇ 25, which one of the following is correct?</p>
<p>(a) <i>a</i> > <i>b</i></p>
<p>(b) <i>a</i> = <i>b</i></p>
<p>(c) <i>a</i> < <i>b</i></p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Convert to natural logarithms and compare the relative magnitudes of the quotients.
<p>Using change of base: <i>a</i> = log₃ 5 = (ln 5)/(ln 3) and <i>b</i> = log₁₇ 25 = (ln 25)/(ln 17) = (2ln 5)/(ln 17). Compare the ratios to determine which is larger.</p>
Correct Answer: A