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Rewrite the expression inside the logarithm in terms of base 3.

April 25, 2026Chemistry

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Answer

\frac{3}{2}

4 steps

Rewrite the expression inside the logarithm in terms of base 3.
We have $3\sqrt{3}$ .
Recall that $\sqrt{3} = 3^{1/2}$ .
So, $3\sqrt{3} = 3^1 \times 3^{1/2}$ .
Use the exponent rule $a^m \times a^n = a^{m+n}$ to combine the terms.
$3^1 \times 3^{1/2} = 3^{1 + \frac{1}{2}} = 3^{\frac{2}{2} + \frac{1}{2}} = 3^{\frac{3}{2}}$
Substitute this back into the original logarithm equation.
$\log_3 (3^{\frac{3}{2}}) = x$
Use the logarithm property $\log_b (b^n) = n$ .
In this case, $b=3$ and $n=\frac{3}{2}$ .
Therefore,
$x = \frac{3}{2}$
The value of $x$ is:
$\frac{3}{2}$

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