How solve complicated logarithm?

enter image source here

Can't someone please explain to me how to do question 6e and 10b? Thank!

1 Answer
Oct 3, 2017

Use definitions

Explanation:

6 e )
log_3(x^2-3x-1) = 0

Take 3^f both sides. You get

3^(log_3(x^2-3x-1)) = 3^0

x^2-3x-1 = 1

Now solve the quadratic equation

x^2-3x-2 = 0

x = (3\pm sqrt(9-4(-2)(1)))/2

x = (3\pm sqrt(17))/2

x = (3+4.1231)/2,(3-4.1231)/2

x = -0.5616,3.5616 (upto 5 significant figures)

10 b)
log_10(5x)-log_10(3-2x)=1

log_10((5x)/(3-2x))=1

Take antilog both sides

(5x)/(3-2x) = 10

5x = 30 - 20x

25x = 30

x = 6/5