# How do you write 9^(3/2)=27 in logarithmic form?

##### 2 Answers
Jan 8, 2017

${\log}_{9} \left(27\right) = \frac{3}{2}$

#### Explanation:

Compare to a known condition

Suppose we had $\text{ } {\log}_{10} \left(x\right) = y$

This is the same as $\text{ "10^y=x" " ul(vec("compare to"))" } {9}^{\frac{3}{2}} = 27$

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So in the case of the question:

Instead of log to base 10 $\to {\log}_{10}$ we have log to base 9$\to {\log}_{9}$

For the index of $y$ we have $\frac{3}{2}$

For the answer of $x$ we have 27

Jan 8, 2017

${\log}_{9} 27 = \frac{3}{2}$

#### Explanation:

${\log}_{a} b = c$ can be changed to ${a}^{c} = b$

For the logarithmic function ${9}^{\frac{3}{2}} = 27$

$a = 9$
$b = 27$
$c = \frac{3}{2}$

This can become

${\log}_{9} 27 = \frac{3}{2}$