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

April 25, 2026Chemistry

ScanSolve AI Answer

April 25, 2026

Answer

$\frac{3}{2}$

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.

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Quick Answer

Rewrite the expression inside the logarithm in terms of base 3. We have 3sqrt(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.

ScanSolve AI AnswerAnswered on April 25, 2026

Step 1: Rewrite the expression inside the logarithm in terms of base 3. We have 3sqrt(3). Recall that sqrt(3) = 3^1/2. So, 3sqrt(3) = 3^1 × 3^1/2. Step 2: Use the exponent rule a^m × a^n = a^m+n to combine the terms. 3^1 × 3^1/2 = 3^1 + (1)/(2) = 3^(2)/(2) + (1)/(2) = 3^(3)/(2) Step 3: Substitute this back into the original logarithm equation. _3 (3^(3)/(2)) = x Step 4: Use the logarithm property _b (b^n) = n. In this case, b=3 and n=(3)/(2). Therefore, x = (3)/(2) The value of x is: (3)/(2) That's 2 down. 3 left today — send the next one.

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.

ScanSolve AI AnswerAnswered on April 25, 2026

Step 1: Rewrite the expression inside the logarithm in terms of base 3. We have 3sqrt(3). Recall that sqrt(3) = 3^1/2. So, 3sqrt(3) = 3^1 × 3^1/2. Step 2: Use the exponent rule a^m × a^n = a^m+n to combine the terms. 3^1 × 3^1/2 = 3^1 + (1)/(2) = 3^(2)/(2) + (1)/(2) = 3^(3)/(2) Step 3: Substitute this back into the original logarithm equation. _3 (3^(3)/(2)) = x Step 4: Use the logarithm property _b (b^n) = n. In this case, b=3 and n=(3)/(2). Therefore, x = (3)/(2) The value of x is: (3)/(2) That's 2 down. 3 left today — send the next one.