### Home > A2C > Chapter 11 > Lesson 11.2.3 > Problem11-77

11-77.

Use the properties of logarithms to rewrite each equation and then solve. Check for extraneous roots.

1. $\operatorname{log}\left(x\right) + \operatorname{log}\left(x + 21\right) = 2$

$\operatorname{log}\left(x^{2} + 21x\right) = 2$

$x^{2} + 21x = 10^{2}$

$\left(x − 4\right)\left(x + 25\right) = 0$

$4$

1. $2\operatorname{log}_{4}\left(x\right) − \operatorname{log}_{4}\left(3\right) = 2$

$\text{log}_4\left(\frac{x^2}{3}\right)=2$

1. $\operatorname{log}_{2}\left(9x + 5\right) − \operatorname{log}_{2}\left(x^{2} − 1\right) = 2$

$\text{log}_2 \left(\frac{9x+2}{x^{2}-1}\right)=2$

$3$

1. $\operatorname{log}_{7}\left(x + 1\right) + \operatorname{log}_{7}\left(x − 5\right) = 1$

See parts (a) and (b).