Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).

Assessment: WAEC SSCE - Further Mathematics - 2010 (Objective) Subject: Further Mathematics

Question 1 Report

Simplify \(\frac{\log_{5} 8}{\log_{5} \sqrt{8}}\).

Answer Details
We can use the properties of logarithms to simplify this expression. Recall that \(\log_{a} b^{c} = c\log_{a} b\) and \(\log_{a} \sqrt{b} = \frac{1}{2}\log_{a} b\). So, \[\frac{\log_{5} 8}{\log_{5} \sqrt{8}} = \frac{\log_{5} 8}{\frac{1}{2}\log_{5} 8} = \frac{2\log_{5} 8}{\log_{5} 8} = \boxed{2}.\] Therefore, the answer is 2.
Read lesson note on Indices And Logarithmic Functions (WAEC)
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