Question

If
$log_{4}(256) + log_{3}(81) - log_{2}(x) = 0$
,then x =​

Answer 1

$Given \: log_{4}(256) + log_{3}(81) - log_{2}(x) = 0$

$\implies log_{4}(4^{4}) + log_{3}(3^{4}) - log_{2}(x) = 0$

$\implies 4 log_{4} 4 + 4 log_{3} 3- log_{2}(x) = 0$

$\boxed { \pink { Since, log_{a} m^{n} = n log_{a} m }}$

$\implies 4 + 4 = log_{2}(x)$

$\blue { (Since , log_{a} a = 1 ) }$

$\implies 8 = log_{2}(x)$

$\implies 2^{8} = x$

$\implies x = 256$

Therefore.,

$\red { Value \:of \: x } \green { = 256 }$

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