Question

(2log5+log4^2+3log2)-2=mlog2 find m

Answer 1

Answer:

5

Step-by-step explanation:

Simplify as (log25+ log16+log8) - 2log10

Log(25*16*8)-log100 =log(3200/100) =log32 = 5log2

Answer 2

$\red{ \huge{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{\mid}}}}}}}}$

$\underline{ \underline{ \bold{ \: \: GIVEN \: \: }}} \to \\ \\ \bold{(2 \: log \: 5 \: + \: log \: 4 {}^{2} \: + \: 3 \: log \: 2) - 2 = \: m \: log \: 2 } \\ \\ \underline{ \underline{ \bold{ \: \: TO \: \: FIND \: \: }}} \to \: \: \: \: \: \bold{Value \: \: of \: \: m = ? }$

$\bold{(2 \: log \: 5 \: + \: log \: 4 {}^{2} \: + \: 3 \: log \: 2 ) - 2= \: m \: log \: 2 } \\ \\ \bold{ \Longrightarrow \:(2 \: log \: 5 \: + \: log \: 4 {}^{2} \: + \: 3 \: log \: 2 ) -2 \: log \: 10 = m\: log \: 2} \\ \\ \bold{ \Longrightarrow \: (\: log \: 5 {}^{2} \: + \: log \: 16\: + \: log \: 2 {}^{3} ) - log \: 10 {}^{2} = \: m \: log \: 2} \\ \\ \bold{ \Longrightarrow \: (log \:25 \: + \: log \: 16 \: + \: log \: 8) - log \:100 \: = \: m \: log \: 2 } \\ \\ \bold{ \Longrightarrow \: log(25 \times 16 \times 8) - log \: 100 = m \: log \: 2} \\ \\ \bold{ \Longrightarrow \: log \: 3200 - \: log \: 100 = m \: log \: 2} \\ \\ \bold{ \Longrightarrow \: log \: ( \frac{3200}{100})= m \: log \: 2 } \\ \\ \bold{ \Longrightarrow \: log \: 32 = m \: log \: 2} \\ \\ \bold{ \Longrightarrow \: log \: (2) {}^{5} = m \: log \: 2 } \\ \\ \bold{ \Longrightarrow \: 5 \: \cancel{log \: 2 }= m \: \cancel{log \: 2}} \\ \\ \bold{ \Longrightarrow \: 5 = m} \\ \\ \bold{ \therefore \: \underline{ \: \: m \: = \: 5 \: \: }}$