QuestionWrite the expression as a single logarithm. $$\frac{1}{3} \log _{c} x+3 \log _{c} y-\log _{c} z$$

Studdy Solution
Combine the logarithmic terms using the product and quotient rules. The product rule states that $\log_b M + \log_b N = \log_b (M \cdot N)$, and the quotient rule states that $\log_b M - \log_b N = \log_b \left(\frac{M}{N}\right)$.
Combine the first two terms using the product rule: $$\log_{c} x^{1/3} + \log_{c} y^3 = \log_{c} (x^{1/3} \cdot y^3)$$
Now, combine with the third term using the quotient rule: $$\log_{c} (x^{1/3} \cdot y^3) - \log_{c} z = \log_{c} \left(\frac{x^{1/3} \cdot y^3}{z}\right)$$
The expression as a single logarithm is: $$\log_{c} \left(\frac{x^{1/3} \cdot y^3}{z}\right)$$