Question

1 use the properties of logarithms to rewrite the expression. Assume all variables represent real numbers

2 Find all rational zeros & factor f(x) 

f(x) = 4x³ –28x² - x + 7

Answer 1

SOLUTION :

1.

log b (m^2 p^8 / (n^9 b^7)

= log b + 2 log m + 8 log p - 9 log n - 7 log b

= 2 log m + 8 log p - 9 log n - 6 log b. (ANSWER)

2.

f(x) 

= 4x^3 - 28x^2 - x + 7 

= 4x^2(x - 7) - 1 (x - 7)

= (x - 7)(4x^2 - 1) = 0

= (x - 7)(2x - 1)(2x + 1)  (Factors of f(x) (ANSWER)

For zeros, set f(x) = 0

=> (x - 7)(2x - 1)(2x + 1) = 0

=> x = 7, 1, - 1 

=> Zeros are : x = - 1, 1, 7 (ANSWER)