How do you write $9^{\frac{3}{2}} = 27$ $9^(3/2) = 27$ in log form?

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How do you write $9^{\frac{3}{2}} = 27$ $9^(3/2) = 27$ in log form?

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Answer 1 · 2015-06-16T21:49:22

${log}_{9} (27) = \frac{3}{2}$ $log_{9}(27)=3/2$

Explanation:

For $b > 0$ $b>0$ , $b \neq 1$ $b!=1$ and $y > 0$ $y>0$ , the symbol $x = {log}_{b} (y)$ $x=log_{b}(y)$ represents the unique real number such that $b^{x} = y$ $b^{x}=y$ (it's the unique solution of that equation).

Since $x = \frac{3}{2}$ $x=3/2$ is the unique solution of the equation $9^{x} = 27$ $9^{x}=27$ , it follows that ${log}_{9} (27) = \frac{3}{2}$ $log_{9}(27)=3/2$ .

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How do you write $9^{\frac{3}{2}} = 27$ $9^(3/2) = 27$ in log form?

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