Simplify the numerator using the logarithm property a^n = n a.
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 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 $\boxed{3}$.
