# Thread: A little bit of help

1. ## A little bit of help

I am trying to solve these questions but i am having trouble

- Find exact value of the following

1) Log86-log83+log84

2) When x^4 - 4x^3 + ax^2 + bx + 1 is divided by (x-1) the remainder is 7
When it is divided by (x+1) the remainder is 3

Determine values of a and b

2. Originally Posted by Infiniti
I am trying to solve these questions but i am having trouble

- Find exact value of the following

1) Log86-log83+log84
$\displaystyle \log_8 6 - \log_8 3 + \log_8 4 = \log_8 \left( \frac {6 \cdot 4}3 \right) = \log_8 8$

can you continue? (you should memorize the rules for logarithms so you know how to simplify them )

2) When x^4 - 4x^3 + ax^2 + bx + 1 is divided by (x-1) the remainder is 7
When it is divided by (x+1) the remainder is 3

Determine values of a and b
use the remainder theorem:

let $\displaystyle f(x) = x^4 - 4x^3 + ax^2 + bx + 1$

then, we know by the remainder theorem, that:

$\displaystyle f(1) = 7$

and

$\displaystyle f(-1) = 3$

you can use this to set up two simultaneous equations where you can solve for a and b