Here's how to simplify the expression: f) Simplify log₁₀ 3√(3) Step 1: Rewrite the argument of the logarithm, 3√(3), as a single power of 3. Recall that √(3) = 3^(1/2). 3√(3) = 3¹ × 3^(1/2); Using the exponent rule a^m × aⁿ = a^(m+n): 3¹ × 3^(1/2) = 3^(1 + 1/2) = 3^(2/2 + 1/2) = 3^(3/2) Step 2: Substitute this back into the logarithm. log₁₀ (3^(3/2)) Step 3: Apply the logarithm power rule, log_b (x^p) = p log_b x. log₁₀ (3^(3/2)) = 3/2 log₁₀ 3 The simplified expression is 3/2 log₁₀ 3.

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Simplify 10 3sqrt(3)

May 16, 2026Mathematics

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Answer

\frac{3}{2} \log_{10} 3

Step-by-step solution

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Here's how to simplify the expression:

f) Simplify $\log_{10} 3\sqrt{3}$

Rewrite the argument of the logarithm, $3\sqrt{3}$ , as a single power of 3.
Recall that $\sqrt{3} = 3^{1/2}$ .
$3\sqrt{3} = 3^1 \times 3^{1/2}$
Using the exponent rule $a^m \times a^n = a^{m+n}$ :
$3^1 \times 3^{1/2} = 3^{1 + \frac{1}{2}} = 3^{\frac{2}{2} + \frac{1}{2}} = 3^{\frac{3}{2}}$
Substitute this back into the logarithm.
$\log_{10} (3^{\frac{3}{2}})$
Apply the logarithm power rule, $\log_b (x^p) = p \log_b x$ .
$\log_{10} (3^{\frac{3}{2}}) = \frac{3}{2} \log_{10} 3$
The simplified expression is $\frac{3}{2} \log_{10} 3$ .

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Simplify 10 3sqrt(3)

Answer

Step-by-step solution

Rewrite the argument of the logarithm, 333\sqrt{3}33​, as a single power of 3.

Substitute this back into the logarithm.

Apply the logarithm power rule, log⁡b(xp)=plog⁡bx\log_b (x^p) = p \log_b xlogb​(xp)=plogb​x.

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More Mathematics Questions

Rewrite the argument of the logarithm, $3\sqrt{3}$ , as a single power of 3.

Apply the logarithm power rule, $\log_b (x^p) = p \log_b x$ .