Explain why the graphs are different

Question

The graphs of [y=log x + log (2x)] and [y=log (2x²)] are different. Although the graphs are different, simplifying the first expression using the laws of logarithms produces the second expression. Explain why the graphs are different.

Answer 1

y = log(x) + log(2x)

   = log(2x^2)

 

Yes, that is correct

 

But, y= log(x) + log(2x)

Here log(x). & log (2x). both are not defined for x negative values

 

While log(2x^2)

 

is defined for x negative values