Question

Prove that $\log (1+2+3)=\log 1+\log 2+\log 3.$

Answer 1

As we can write $\log (1+2+3)=\log 6$

Also $\log 6=\log (1\times 2\times 3)$

As we know that $\log \left(ab\right)=\log a+\log b$

$$\begin{gathered} \Rightarrow \log \left(abc\right)=\log a+\log b+\log c \\ \Rightarrow \log (1\times 2\times 3)=\log 1+\log 2+\log 3 \end{gathered}$$

Hence proved.