Question

Expand the given logarithmic expression \[\log (15)\].

Answer 1

Hint: Use the logarithmic property that is given as \[\log (a\times b)=\log a+\log b\]. Here 15 can be written as \[3\times 5\].

Complete step-by-step answer:
In the given problem, we have to find the expansion of \[\log (15)\].
Here the base of the logarithm can be anything, but there will be no change in the formula that is \[\log (a\times b)=\log a+\log b\]

Now, we can write 15 as \[3\times 5\]. Hence, we have:
\[\Rightarrow \log (15)=\log (3\times 5)\]
Next using the formula \[\log (a\times b)=\log a+\log b\], we can write the expansion as:
\[\begin{align}
  & \Rightarrow \log (15)=\log (3\times 5) \\
 & \Rightarrow \log (15)=\log (3)+\log (5) \\
\end{align}\]
Hence, \[\log (3)+\log (5)\] is the required expansion form of \[\log (15)\].

Note: The properties of logarithms are crucial in solving such problems. We have to keep in mind that the formula is \[\log (a\times b)=\log a+\log b\] and should also remember that in most cases \[\log (a+b)\ne \log a+\log b\].