### Home > CCA2 > Chapter 9 > Lesson 9.1.2 > Problem9-27

9-27.

Solve each equation.

1. $\text{log}_{2}(x)+\text{log}_{2}(x-2)=3$

Combine into one log on the left side. Then undo on both sides.

$2^{\log_{2}\left(\left(x\right)\left(x-2\right)\right)}=2^{3}$

$\log_{2}\left(\left(x\right)\left(x-2\right)\right)=3$

$(x)(x-2)=8$

$x^{2}-2x-8=0$

$(x-4)(x+2)=0$

$x=4\text{ or }x=-2$  (log input must be positive)

1. $\text{log}(2x)-\text{log}(x^2)=-2$

Follow a similar process as part (a). Don't forget that the ($−$) sign means to divide the terms instead of multiply!