Question

which equation is equivalent to \\(\log 5x^3 - \log x^2 = 2\\)?
\\(\circ\\) \\(10^{\log 5x^4} = 10^2\\)
\\(\circ\\) \\(10^{\log \frac{5x^3}{x^2}} = 10^2\\)
\\(\circ\\) \\(10^{\log \frac{5x^3 + x^3}{x^2}} = 10^2\\)
done

Explanation:

Step1: Recall Logarithm Subtraction Rule

The logarithm subtraction rule states that $\log a - \log b = \log \frac{a}{b}$. For the equation $\log 5x^3 - \log x^2 = 2$, apply this rule: $\log \frac{5x^3}{x^2}=2$.

Step2: Apply Exponentiation with Base 10

To eliminate the logarithm, exponentiate both sides with base 10 (since $\log$ here is base 10, though not specified, standard practice). So, $10^{\log \frac{5x^3}{x^2}} = 10^2$.

Answer:

The second option: $10^{\log \frac{5x^3}{x^2}} = 10^2$