Question

log x =log3 + 2log2 - 3/4log16

solve the question

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Answer 1

Step-by-step explanation:

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Answer 2

Given:-

• $\sf \: log(x) = log(3) + 2 log(2) - \dfrac{3}{4} log(16)$

To find:-

• The value of x

Answer:-

Given that,

$\sf \: log(x) = log(3) + 2 log(2) - \dfrac{3}{4} log(16)$

$\red \bigstar \boxed{ \sf{a log(b) = log( {b}^{a} ) }}$

$\sf \longrightarrow log(x) = log(3) + log(2 {}^{2} ) - log(16 {}^{3/4} )$

$\sf \longrightarrow log(x) = log(3) + log(4 ) - log \{( { {2}^{4}) }^{3/4} \}$

$\sf \longrightarrow log(x) = log(3) + log(4 ) - log( {2}^{3} )$

$\sf \longrightarrow log(x) = log(3) + log(4 ) - log( 8 )$

$\blue \bigstar \boxed{ \sf{ log(a) + log(b) = log( ab ) }}$

$\sf \longrightarrow log(x) = log(3 \times 4) - log( 8 )$

$\sf \longrightarrow log(x) = log(12) - log( 8 )$

$\green \bigstar \boxed{ \sf{ log(a) - log(b) = log \Bigg( \dfrac{a}{b} \Bigg) }}$

$\sf \longrightarrow log(x) = log\Big( \dfrac{12}{8} \Big)$

$\sf \longrightarrow log(x) = log \Big( \dfrac{3}{2} \Big)$

On comparing both sides,

$\longrightarrow \underline{ \underline{ \sf{ \green{ x = \dfrac{3}{2} }}}}$