Question

5log[3]x-3log[3]y+log[3]z
write the expression as a single logarithm

Answer 1

Hmm.... I have honestly forgotten how to do these, BUT... when you write [3], that refers to our base, yes?

Answer 2

yes

Answer 3

Awesome. To the best of my knowledge:

Answer 4

You take the 5log[3]x
And change it to log[3]x^5

3log[3]y, change it to log[3]y^3

log[3]z leave it as is.

Now... if I recall correctly, it's log[3] ((x^5/y^3)*(z))

however.... wait till someone else posts to be safe.

Answer 5

log[a]x=lnx/lna
clog[a]x=log[a]x^c

Answer 6

^ I've got that part already. We need to double check the log addition to multiplication rule and the log subtraction to division rule.

Answer 7

I'm just not sure what the 'order of operations" would be for log - log + log. I *think* it's left to right, so log((?/?)*(?)) but I'm iffy on that.

Answer 8

log[a]x+log[a]y=log[a](xy)=ln(xy)/lna
log[a]x-log[a]y=log[a](x/y) so just use those

Answer 9

Ya, but I mean what about the order? Do we just assume left to right?

Answer 10

either way your going to get the right answer. i would add first then subtrack but up to you

Answer 11

Oh. Division is commutative? Didn't realize that. Haha. Oh dear... and I'm going into cal 2 in only a few months. Better brush up on my 4th grade math rules. :P