Question

Guys please help me out with the question in the attachment ASAP. I really need your help. Don't spam. ​

Answer 1

$\Large\star{\underline{\tt{\red{Given}}}}\star$:-

$\bigstar\bf\:a = 2 + 4 log_{10}(2) - 2 log_{10}(5) \\ \\\bigstar\bf\:b=4 log_{10}(3) \\ \\\bigstar\bf\:c =log_{10}(m) - log_{10}(5) \\ \\\bigstar\bf\:a + b = 2c$

Tᴏ Fɪɴᴅ :-

• Value of m ?

$\Large\bold\star\underline{\underline\textbf{Formula\:used}}$ :-

● $\orange{\bf{Product\:Rule\:Law:}}$

→ loga (MN) = loga M + loga N

● $\pink{\bf{Quotient\:Rule\:Law:}}$

→ loga (M/N) = loga M - loga N

● $\green{\bf{Power\:Rule\:Law:}}$

→ IogaM^(n) = n Ioga M

$\Large{\mathfrak{\overbrace{\underbrace{\pink{\fbox{\green{\blue{\bf\:S}\pink{o}\red{l}\orange{u}\purple{t}\blue{i}\green{o}\red{n}}}}}}}}$

Putting values in a + b = 2c , we get :-

$\red\leadsto\footnotesize\:2+4 log_{10}(2)-2 log_{10}(5)+4 log_{10}(3)=2(log_{10}(m)-log_{10}(5)) \\ \\ \footnotesize\: putting \: 2 = log_{10}(100) \: in \:LHS \: and \: using \: power \: rule \\ \\\red\leadsto\footnotesize\: log_{10}(100) +log_{10}(2)^{4} - log_{10}(5)^{2} + log_{10}(3)^{4} =2(log_{10}(m)-log_{10}(5)) \\ \\\red\leadsto\footnotesize\:log_{10}[ \frac{100\times{2}^{4}\times{3}^{4}}{ {5}^{2}}] =2log_{10}(\frac{m}{5})\\\\\red\leadsto\footnotesize\:log_{10}(4 \times 16 \times 81) = log_{10}(\frac{m^{2}}{25})\\\\\red\leadsto\footnotesize\:{m}^{2}=4 \times 16 \times 81 \times 25\\\\\red\leadsto\footnotesize \: m = 2 \times 4 \times 9 \times 5\\\\\red\leadsto \:\bold{\boxed{{\boxed{\orange{\small{\boxed{\huge{\red{\bold{\huge\bold{\red{m=360}}}}}}}}}}}}$

$\rule{200}{4}$