How do you evaluate $log_9 x=3/2$ ?

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Answer 1 · 2016-10-27T11:19:50

$x=27$

Remember that in general $log_b a = c$ means $b^c=a$
(You really need to memorize this; it's a basic definition.)

Therefore $log_9 x=3/2$
means
$color(white)("XXX")9^(3/2)=x$

$rarrcolor(white)("XX")x=9^(3/2)$

$color(white)("XXXX")=(9^(1/2))^3$

$color(white)("XXXX")=(+3)^3$ (the negative root can be ignored since log arguments must be positive)

$color(white)("XXXX")=27$

How do you evaluate log_9 x=3/2log_9 x=3/2?