How do you solve ${log}_{36} x = \frac{1}{2}$ $log_36x= 1/2$ ?

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Answer 1 · 2015-12-13T19:44:53

$x = 6$ $x= 6$

${log}_{36} x = \frac{1}{2}$ $log_(36) x = 1/2$

Switch to exponential form of ${log}_{a} x = y \Leftrightarrow a^{y} = x$ $log_a x= y <=> a^y = x$

${log}_{36} x = \frac{1}{2}$ $log_(36)x= 1/2$
$\Rightarrow {(36)}^{\frac{1}{2}} = x$ $=> (36)^(1/2) = x$
$\Rightarrow \sqrt{36} = x$ $=> sqrt(36)= x$

=> $x = 6$ $x= 6$

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