Simplify the numerator using the logarithm property a^n = n a.

April 1, 2026Mathematics

ScanSolve AI Answer

April 1, 2026

Answer

To simplify the expression $\frac{\log 27}{\log 6 - \log 2}$ :

Step 1: Simplify the numerator using the logarithm property $\log a^n = n \log a$ . $\log 27 = \log (3^3) = 3 \log 3$

Step 2: Simplify the denominator using the logarithm property $\log a - \log b = \log \left(\frac{a}{b}\right)$ . $\log 6 - \log 2 = \log \left(\frac{6}{2}\right) = \log 3$

Step 3: Substitute the simplified numerator and denominator back into the original expression. $\frac{3 \log 3}{\log 3}$

Step 4: Cancel out the common term $\log 3$ . $3$ The simplified expression is $\boxed{3}$ .

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Quick Answer

To simplify the expression ( 27)/( 6 - 2): Step 1: Simplify the numerator using the logarithm property a^n = n a.

Asked on April 1, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 1, 2026

To simplify the expression ( 27)/( 6 - 2): Step 1: Simplify the numerator using the logarithm property a^n = n a. 27 = (3^3) = 3 3 Step 2: Simplify the denominator using the logarithm property a - b = ((a)/(b)). 6 - 2 = ((6)/(2)) = 3 Step 3: Substitute the simplified numerator and denominator back into the original expression. (3 3)/( 3) Step 4: Cancel out the common term 3. 3 The simplified expression is 3.