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

Question

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

Asked on April 25, 2026Chemistry

This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.

Accepted Answer · 2026-04-25T17:16:42.336Z

Step 1: Rewrite the expression inside the logarithm in terms of base 3. We have $3\sqrt{3}$. Recall that $\sqrt{3} = 3^{1/2}$. So, $3\sqrt{3} = 3^1 \times 3^{1/2}$. Step 2: Use the exponent rule $a^m \times a^n = a^{m+n}$ to combine the terms. $$3^1 \times 3^{1/2} = 3^{1 + \frac{1}{2}} = 3^{\frac{2}{2} + \frac{1}{2}} = 3^{\frac{3}{2}}$$ Step 3: Substitute this back into the original logarithm equation. $$\log_3 (3^{\frac{3}{2}}) = x$$ Step 4: 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: $$\boxed{\frac{3}{2}}$$ That's 2 down. 3 left today — send the next one.

Accepted Answer · 2026-04-25T17:16:42.336Z

Step 1: Rewrite the expression inside the logarithm in terms of base 3. We have $3\sqrt{3}$. Recall that $\sqrt{3} = 3^{1/2}$. So, $3\sqrt{3} = 3^1 \times 3^{1/2}$. Step 2: Use the exponent rule $a^m \times a^n = a^{m+n}$ to combine the terms. $$3^1 \times 3^{1/2} = 3^{1 + \frac{1}{2}} = 3^{\frac{2}{2} + \frac{1}{2}} = 3^{\frac{3}{2}}$$ Step 3: Substitute this back into the original logarithm equation. $$\log_3 (3^{\frac{3}{2}}) = x$$ Step 4: 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: $$\boxed{\frac{3}{2}}$$ That's 2 down. 3 left today — send the next one.

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