Mathematics - Basic maths Question with Solution | TestHub

MathematicsBasic mathsLogarithmMedium2 minPYQ_2017

MathematicsMediumsingle choice

If $a = \log_{2} 3, b = \log_{2} 5$ and $c = \log_{7} 2$ , then $\log_{140} 63$ in terms of $a, b, c$ is

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Answer:

Solution:

We have,

$\log_{140} 63 = \log_{2^{2} \times 5 \times 7} (3 \times 3 \times 7)$

$= \frac{\log_{2} (3 \times 3 \times 7)}{\log_{2} (2^{2} \times 5 \times 7)} = \frac{\log_{2} 3 + \log_{2} 3 + \log_{2} 7}{2 \log_{2} 2 + \log_{2} 5 + \log_{2} 7}$

$= \frac{2 a + \frac{1}{c}}{2 + b + \frac{1}{c}} = \frac{2 a c + 1}{2 c + b c + 1}$

Stream:JEESubject:MathematicsTopic:Basic mathsSubtopic:Logarithm

⏱ 2mℹ️ Source: PYQ_2017

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