Question

write as a single logarithm:
log(base 3)sq.rt.X-log(base 3)x^3?

Answer 1

\[\Large \log_3 \sqrt x - \log_3 x^3\]

now...are you familiar that.. \[\large \log_a b - \log_a c = \log_a (\frac{b}{c})??\]

Answer 2

yeah and so the next step would be sq.rt.x/x^3 right? And square root x is the same as x^1/2

Answer 3

yep! you're good :D

Answer 4

dont forget log (base 3) somewhere there

Answer 5

\[\large \log_3 (\frac{\sqrt x}{x^3}) \implies \log_3 (\frac{x^{1/2}}{x^3}) \implies \log_3 (x^{(1/2) - 3})\] understood?

Answer 6

yeah and so 1/2 - 6/2 is 5/2, how does it become 1/x^5/2?

Answer 7

yep :DD

Answer 8

note that \[\LARGE x^{5/2} \implies \sqrt {x^5} \implies x^2 \sqrt x\]

Answer 9

Ohhh ok I gotcha, thanks a lot!

Answer 10

but personally...i think \[\large \log_3 (\frac{\sqrt x}{x^3})\] is enough because remember how you're not supposed to have square roots in denominators? therefore you're gonna have to rationalize that answer we have in the previous post and it comes back to this one lol

Answer 11

Hmm good point lol well the asnwer in the back was left as 5/2 in the denominator, so I guess that wouldnt require it to go back?

Answer 12

well \[\large \log_3 (\frac{\sqrt x}{x^3}) = \log_3 (\frac{1}{x^{5/2}}) = \log_3 (\frac{1}{\sqrt x^5}) = \log_3 (\frac{1}{x^2 \sqrt x})\] they are all correct they jsut differ in forms...

Answer 13

yeah true, I think they just didn't want any square roots left in the answer. I know on our test he wants everything simplified as far as possible so ill go with that lol thanks for explaining it all!

Answer 14

thanks for being an awesome student ^_^ <tips hat>