If log 3 5 = a and log 3 2 = b , then log 3 300

Question

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

Smart Achievers · Accepted Answer

(2)

$\log_{\sqrt{3}} 5 = a,$ $\log_{\sqrt{3}} 2 = b$

$\log_{\sqrt{3}} 5 + \log_{\sqrt{3}} 2 = a + b,$ $\log_{\sqrt{3}} 10 = a + b$

$\log_{\sqrt{3}} 300 = \log_{\sqrt{3}} (3 \cdot 100) = \log_{\sqrt{3}} 3 + \log_{\sqrt{3}} {(10)}^{2}$

$= \log_{\sqrt{3}} {(\sqrt{3})}^{2} + 2 \log_{\sqrt{3}} 10 = 2 + 2 (a + b) = 2 (a + b + 1)$

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