Let a = ((_7 4)(_7 5 - _7 2))/(_7 25 (_7 8 - _7 4)). Then the value of 5^a is Option 1: 8 Option 2: 5/2 Option 3: 5 Option 4: 7/2

Answer: 5/2. Solution: You might be wondering how (_7 52)/(_7 5) = _5 52. Property used = _a m = (_b m)/(_b a) In logarithm, you need to not just know how LHS -> RHS (in terms of the properties), but also how RHS -> LHS.

Modern Math

Logarithms

Medium

Let $a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}$ . Then the value of $5^a$ is

$\frac{5}{2}$

$\frac{7}{2}$

✅ Correct Option: 2

Solution figure for IPMAT Indore 2024 MCQ question 8 (Modern Math)

You might be wondering how $\dfrac{\log_7 \frac52}{\log_7 5} = {\log_5 \frac52}$ .

Property used $=\boxed{ {\log_a m} = \dfrac{\log_b m}{\log_b a}}$

In logarithm, you need to not just know how LHS -> RHS (in terms of the properties), but also how RHS -> LHS.

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Let a=(log⁡74)(log⁡75−log⁡72)log⁡725(log⁡78−log⁡74)a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}a=log7​25(log7​8−log7​4)(log7​4)(log7​5−log7​2)​. Then the value of 5a5^a5a is

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IPMAT Indore Past Year Questions (Topic-Wise)

Let $a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}$ . Then the value of $5^a$ is