Question 7 of 10 Write the following expression as a sum and/or difference of logarithms. Express powers as factors. \[ \log _{c}\left(u^{3} v^{8}\right) \quad u>0, v>0 \] $\log _{c}\left(u^{3} v^{8}\right)=\square($ Simplify your answer. $)$

Step 1 ：The given expression is a logarithm of a product. According to the properties of logarithms, the logarithm of a product is equal to the sum of the logarithms of the individual factors.

Step 2 ：Also, the logarithm of a power is equal to the product of the exponent and the logarithm of the base.

Step 3 ：Therefore, we can rewrite the given expression as a sum of logarithms, where the powers are expressed as factors.

Step 4 ：\[ \log _{c}\left(u^{3} v^{8}\right) = 3\log _{c}(u) + 8\log _{c}(v) \]

Step 5 ：\(\boxed{ \log _{c}\left(u^{3} v^{8}\right) = 3\log _{c}(u) + 8\log _{c}(v) }\)