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

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Answer 1 · 2017-01-08T20:24:30

$log_9(27)=3/2$

Compare to a known condition

Suppose we had $" "log_10(x)=y$

This is the same as $" "10^y=x" " ul(vec("compare to"))" " 9^(3/2)=27$

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So in the case of the question:

Instead of log to base 10 $-> log_10$ we have log to base 9 $-> log_9$

For the index of $y$ we have $3/2$

For the answer of $x$ we have 27

Answer 2 · 2017-01-08T21:32:58

$log_9 27 = 3/2$

$log_ab= c$ can be changed to $a^c = b$

For the logarithmic function $9^(3/2) = 27$

$a = 9$
$b = 27$
$c = 3/2$

This can become

$log_9 27 = 3/2$

How do you write 9^(3/2)=279^(3/2)=27 in logarithmic form?