Basic Maths and Logarithm
Properties of Logarithms
JEE Advanced
Grade 11
Question:
If $\log_{10} 5 = a$ and $\log_{10} 3 = b$, then $\log_{30} 8$ equals:
(1) $\frac{3(1 - a)}{b + 1}$
(2) $\frac{3(1 - a)}{1 + b}$
(3) $\frac{3a}{b + 1}$
(4) $\frac{1 - a}{3b}$
Step-by-Step Solution
Key Concept: $\log_{30} 8 = \frac{\log 8}{\log 30} = \frac{3 \log 2}{\log 3 + \log 10} = \frac{3(1 - \log 5)}{\log 3 + 1} = \frac{3(1 - a)}{b + 1}$.
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Correct Answer: (1)