Chapter 5.6, Problem 109DW

Fill in the reason for each step in the following two solutions.

Solve: ${\log }_3{\left(x-1\right)}^2=2$

Solution A

${\log }_3{\left(x-1\right)}^2=2$

${\left(x-1\right)}^2=3^2=9\_\_\_\_\_$

$\left(x-1\right)=\pm 3\_\_\_\_\_$

$x-1=-3$ or $x-1=3\_\_\_\_\_$

$x=-2$ or $x=4\_\_\_\_\_$

Solution B

${\log }_3{\left(x-1\right)}^2=2$

$2{\log }_3\left(x-1\right)=2\_\_\_\_\_$

${\log }_3\left(x-1\right)=1\_\_\_\_\_$

$x-1=3^1=3\_\_\_\_\_$

$x=4\_\_\_\_\_$

Both solutions given in Solution A check. Explain what caused the solution $x=-2$ to be lost in Solution B.