CPM Homework Help : INT3 Problem 11-112

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11-112.

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

$- 4 x ^ { 5 } - 6 = - 1$
Hint (a):
$x=\sqrt[5]{\frac{-5}{4}}$

$- 7 ( 10 ^ { x } ) + 9 = - 5$
Step 1(b):
$10^{x} = 2$

$8 \operatorname { log } _ { 7 } ( 1 + x ) - \operatorname { log } _ { 7 } ( 1 ) = 7$
Hint (c):
$\log_7(1)=0$
Step (c):
$8 \text{log}_{7}\left(1 + x\right) = 7 ⇒ \text{log}_{7} \left(1 + x\right)^{8} = 7$
Answer (c):
$x = 7^{7/8} − 1 ≈ 4.489$

$\frac { 3 } { x } + \frac { 5 } { x + 7 } = - 2$
Hint (d):
Use fraction busters to clear the fractions and then solve the quadratic equation.

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