How do you solve ${log}_{9} x = 1.5$ $log_9x = 1.5$ ?

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How do you solve ${log}_{9} x = 1.5$ $log_9x = 1.5$ ?

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Answer 1 · 2016-06-11T12:23:50

I found $x = 27$ $x=27$

Explanation:

We can write it trying to manipualte $1.5$ $1.5$ into $\frac{3}{2}$ $3/2$ :
${log}_{9} (x) = \frac{3}{2}$ $log_9(x)=3/2$
we use the definition of log:
$x = 9^{\frac{3}{2}}$ $x=9^(3/2)$
and the property of exponents:
$x = \sqrt{9^{3}}$ $x=sqrt(9^3)$
$x = 27$ $x=27$

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How do you solve ${log}_{9} x = 1.5$ $log_9x = 1.5$ ?

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How do you solve ${log}_{9} x = 1.5$ $log_9x = 1.5$ ?