If log-35-a and log-32-b then log-3300-

Explanation for the correct option:Given that log_√(3)(5)=a and log_√(3)(2)=bWe know that log_b(xy)=log_b(x)+log_b(y) So, log_√(3)(300) can be simplified as lo ...

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Standard VIII

Mathematics

Checking Whether nth Root of a Combination of Numbers is a Surd or Not

If log√35=a a...

Question

If $\log_{\sqrt{3}} (5) = a$ and $\log_{\sqrt{3}} (2) = b$ then $\log_{\sqrt{3}} (300) =$

$2 (a + b)$

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$2 (a + b + 1)$

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$2 (a + b + 2)$

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$(a + b + 4)$

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$(a + b + 1)$

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Solution

The correct option is B
$2 (a + b + 1)$

Explanation for the correct option:
Given that $\log_{\sqrt{3}} (5) = a$ and $\log_{\sqrt{3}} (2) = b$
We know that $\log_{b} (x y) = \log_{b} (x) + \log_{b} (y)$
So, $\log_{\sqrt{3}} (300)$ can be simplified as $\log_{\sqrt{3}} (3 \times 10^{2})$
$= \log_{\sqrt{3}} {(\sqrt{3})}^{2} + \log_{\sqrt{3}} {(5 \times 2)}^{2} = 2 \log_{\sqrt{3}} (\sqrt{3}) + 2 [\log_{\sqrt{3}} (5 \times 2)] [∵ \log_{b} {(x)}^{n} = {nlog}_{b} {(x)}^{}] = 2 \log_{\sqrt{3}} (\sqrt{3}) + 2 \log_{\sqrt{3}} (5) + 2 \log_{\sqrt{3}} (2) [∵ \log_{b} (xy) = \log_{b} (x) + \log_{b} (y)] = 2 (1) + 2 (a) + 2 (b) [∵ \log_{b} (b) = 1, \log_{\sqrt{3}} (5) = a, \log_{\sqrt{3}} (2) = b] = 2 (a + b + 1)$
Hence, option(B) i.e. $2 (a + b + 1)$ , is the correct answer.

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If log35=a and log32=b then log3300=

If $\log_{\sqrt{3}} (5) = a$ and $\log_{\sqrt{3}} (2) = b$ then $\log_{\sqrt{3}} (300) =$