First slide

Types of real valued functions XI

Question

If $\frac{a + \log_{4} 3}{a + \log_{2} 3} = \frac{a + \log_{8} 3}{a + \log_{4} 3} = b,$ then b is equal to

Moderate

A

$\frac{1}{2}$
B

$\frac{2}{3}$
C

$\frac{1}{3}$
D

$\frac{3}{2}$

Solution

apply ratio and proportional property
$\frac{a + \log_{4} 3}{a + \log_{2} 3} = \frac{a + \log_{8} 3}{a + \log_{4} 3} = \frac{\log_{4} 3 - \log_{8} 3}{\log_{2} 3 - \log_{4} 3} = \frac{1}{3}$

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