If two quantities are equal, are their logarithms also equal? Consider the questions below.

1. Are the equations $x = 5$ and $\log(x)=\log(5)$ equivalent? Justify your answer.

   Hint (a):

   What solutions satisfy each equation?

2. Is the equation $\log(7) = \log(x^2)$ equivalent to the equation $7 = x^2$? How can you be sure?

   Hint (b):

   See part (a).

   Answer (b):

   Yes. Possible response: Both equations have the same solutions.