Question

Find the value of x, when log base 4 (1/256) = -x/4​

Answer 1

Answer:

x = 16

Step-by-step explanation:

$log_{4}( \frac{1}{256} ) \\ = log_{ {2}^{2} }( {2}^{ - 8} ) \\ = \frac{ - 8}{2} log_{2}(2) \\ = - 4$

-x/4 = -4

x = 16

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Answer 2

Answer:

$\displaystyle{\rightarrow x=16}$

Step-by-step explanation:

Given :

$\displaystyle{\log_4\left(\frac{1}{256}\right)=-\frac{x}{4}}\\\\\\\displaystyle{\log_4\left(\frac{1}{4}\right)^4=-\frac{x}{4}}\\\\\\\displaystyle{4\log_4\left(4^{-1}\right)=-\frac{x}{4}}\\\\\\\displaystyle{-4\log_44=-\frac{x}{4}}\\\\\\\displaystyle{-4=-\frac{x}{4}}\\\\\\\displaystyle{\rightarrow x=16}$