### Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem11-112

11-112.

Solve the following equations. Write your answers in exact form and approximate form, accurate to three decimal places.

1. $- 4 x ^ { 5 } - 6 = - 1$

$x=\sqrt[5]{\frac{-5}{4}}$

1. $- 7 ( 10 ^ { x } ) + 9 = - 5$

$10^{x} = 2$

1. $8 \operatorname { log } _ { 7 } ( 1 + x ) - \operatorname { log } _ { 7 } ( 1 ) = 7$

$\log_7(1)=0$

$8 \text{log}_{7}\left(1 + x\right) = 7 ⇒ \text{log}_{7} \left(1 + x\right)^{8} = 7$

$x = 7^{7/8} − 1 ≈ 4.489$

1. $\frac { 3 } { x } + \frac { 5 } { x + 7 } = - 2$

Use fraction busters to clear the fractions and then solve the quadratic equation.