Question

Help with logs? Find the exact value solution of the equation.
log5 (x+1) - log5 x = log5 7
(btw all of the 5s are the base/small number at the bottom)

Answer 1

apply quotient property \[\huge\rm log_b x \color{red}{-} \log_b y = \log_b \frac{ x }{ y }\]
if there is negative sign you can change that to division
subtraction ---->division
addition .-----> multiplication

Answer 2

Yes I think I understand that, so it would then just be (x+1)/x=7? I thought there was something where you can cancel out the logs if they are the same or something like that. Then you would just solve for x right?

Answer 3

yes right now just solve for x
and yes bec bases are same so you can cancel out log right perfect now solve for x

Answer 4

so I have to get x by itself. So i can cancel out the x/x an be left with 1/x correct? and then flip and have -x and then i would multiply both sides by -1 to get x=-7? or did i mess up in there somewhere?

Answer 5

nope you can't cancel x

Answer 6

By the way, thank you for the medal. Not sure what i use it for, but thank you:)