Express as a single logarithm.
\[
\log _{c}(70)+\log _{c}(25)
\]
\(\boxed{\log _{c}(70)+\log _{c}(25) = \log _{c}(1750)}\)
Step 1 :The problem is asking to express the sum of two logarithms as a single logarithm. The logarithmic property that can be used here is the product rule.
Step 2 :The product rule states that the sum of the logarithms of two numbers is the logarithm of the product of those numbers.
Step 3 :Therefore, we can multiply the numbers inside the logarithms together to get a single logarithm.
Step 4 :\(\log _{c}(70)\) and \(\log _{c}(25)\) can be combined into \(\log _{c}(70 \times 25)\)
Step 5 :So, \(\log _{c}(70)+\log _{c}(25) = \log _{c}(1750)\)
Step 6 :\(\boxed{\log _{c}(70)+\log _{c}(25) = \log _{c}(1750)}\)