### Home > A2C > Chapter 7 > Lesson 7.1.4 > Problem 7-54

7-54.

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

Is it true that 4

^{2}is equal to 2^{4}? Is this a special case, or is*a*equal to^{b}*b*for any values of^{a}*a*and*b*?Is log 4

^{2}equal to log 2^{4}? How can you be sure?Are the equations

*x*= 5 and log*x*= log 5 equivalent?**Justify**your answer.Is the equation log 7 = log

*x*^{2}equivalent to the equation 7 =*x*^{2}? How can you be sure?

Try a few other combinations of *a ^{b}* and

*b*.

^{a}Simplify the exponential expressions first.

What solutions satisfy each equation?

See part (c).