Question

pls full explain this

don't answer only option
​

Answer 1

$\small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}$

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$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$

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$\begin{array}{l} \rm \log _{10} 31.25=\log _{10} \left( \dfrac{ 3125}{ 100} \right) \\ \\ \rm \Rightarrow \log _{10}(3125)-\log _{10}(100) \\ \\ \rm \Rightarrow \log _{10}(5)^{5}-\log _{10}(10)^{2} \\ \\ \rm \Rightarrow 5\left[\log _{10}(5)\right]-2\left[\log _{10}(10)\right] \\ \\ \rm \Rightarrow 5\left[\log _{10} \left( \dfrac{10} {2} \right)\right]-2 \\ \\ \rm \Rightarrow 5\left[\log _{10}(10)-\log _{10}(2)\right]-2 \\ \\ \rm \Rightarrow 5-5\left[\log _{10}(2)\right]-2 \\ \\ \rm \Rightarrow 3-5\left[\log _{10}(2)\right] \\ \\ \boxed{\pink{ \rm \therefore \log _{10} 31.25=3-5 \log _{10} 2}} \end{array}$

Hence, Correct option is (A).