Question

the value of $\log 3+\log 5$ is equal to?

Answer 1

Hint: According to the given question, we need to find the sum of logarithmic functions at two values. Now, this can be done using logarithmic properties that will give us the direct result and hence we will get our required answer. Property of logarithmic function which can be used in this question is $\log m+ \log n=\log mn$ .

Complete step-by-step solution:
In the given question we need to find the sum of two logarithmic functions at two different values. We can directly say after observing the question that we need to apply the property in order to get the answer. Now the logarithmic property that can be directly used in the question is $\log m+ \log n=\log mn$. Now, comparing this identity to the given question we can clearly see that it is exactly the same. All we need to do is just substitute the value or m and n in the identity and attain the answer.
Now, from $\log 3+\log 5$we get that the value of m is 3 and n is 5.
Therefore, applying the above-mentioned identity we get,
$\begin{align}
  & \log 3+\log 5=\log 3\times 5 \\
 & \Rightarrow \log 3+\log 5=\log 15 \\
\end{align}$
Therefore, we can say that $\log 3+\log 5=\log 15$.

Note: In such a type of question, we need to be very careful while applying the properties also we need to take care that properties of logarithmic functions are quite confusing and there are many chances of error. So be more careful while applying those properties also we need to care during the calculation rest such questions are easy to attempt.