Question

find x, if 2log3 + 1/2log4 - log2 = log x

Answer 1

Answer:

log3=0.47

log4=0.60

log2=0.30

2(0.47)+1/2(0.60)-0.30=logx

0.94+1/2(0.60-0.30)=logx

0.94+1/2(0.30)=logx

0.94+0.15=logx

1.09=logx

log(1.09)=x

x=0.03

Answer 2

Question :

Find the value of x,if

2log3 +1/2 log 4 - log 2= logx

Properties of Logarithm:

$1) log \: x {}^{n} = n \: logx$

$2) log(a) + log(b) = log(ab)$

$3) log(a) - log(b) = log( \frac{a}{b} )$

Solution :

We have to find the value of x ,if

$2 log(3) + \frac{1}{2} log(4) - log(2) = log(x)$

use property of $logx{}^{n}=nlogx$

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$\implies log(3 {}^{2} ) + log(4 {}^{ \frac{1}{2} } ) - log(2) = log(x)$

$\implies \: log(9) + log(2) - log(2) = log(x)$

$\implies \: log(9) = log(x)$

⇒on camparing x = 9

${\purple{\boxed{\large{\bold{x=9}}}}}$

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More logarithm Properties :

$1) log_{a {}^{n} }(x) = \frac{1}{n} log_{a}(x)$

$2) log_{a}(b) = \frac{1}{ log_{b}(a) }$

$3) log_{a}(b) = \frac{ log_{e}(b) }{ log_{e}(a) }$