Question

How do you solve ln(5x-1)=ln6-ln(x-6)

Answer 1

you can use the property of log that:

log(a) - log(b) = log(a/b)

ln(5x - 1) = ln(6/(x-6))

take e of both sides

5x - 1 = 6/(x-6)

(5x - 1)(x - 6) = 6.

you can expand the left side and then find the roots with the quadratic formula.

let me know if i you want me to solve for x

Answer 2

other approach: log(a) + log(b) = log(ab). bring the ln(x - 6) to the left. e both sides

Answer 3

thank you so much!!

Answer 4

:)

Answer 5

i'm kind of lost on what you do when you get to the step (5x-1)(x-6)=6

Answer 6

you can expand by multiplying throughout.

5x(x) + 5x(-6) + (-1)x + (-1)(-6) = 6

5x^2 - 31x = 0

Answer 7

maybe you've heard the acronym FOIL

Answer 8

oh yeah i remember that part! so after that do i divide both sides by 5 or do something else?

Answer 9

you can. I would factor out x.

x(5x -31) = 0

this equation is true when x = 0 and when (5x - 31) = 0

Answer 10

so is that the end result or do i have to do more? sorry to keep bothering you!

Answer 11

it's not a bother. i'm here to help people :)

i guess the questions wants you to solve for x.

the answer would b x = 0 and x = 31/5 (obtained from 5x-31 = 0)

Answer 12

thank you so much! :)