Question

write the expression \[\log \sqrt{10xy ^{2}}/z ^{2}\] as a combination of log x, log y and log z. that means break it up completely

Answer 1

i got ½logx + 2log y-2logZ
is that right?

Answer 2

where's the 10? Also you forgot the square for y.

Answer 3

isn't the 10 automatic when its just log? and 2 log y means squared right?

Answer 4

square root, I meant, sorry

Answer 5

so i would put down the ½ twice?
would it look like ½logx + (½)2log y-2logZ?
on my study guide the answer is ½+½logx+logy-2logz…but i don't get how they got that/

Answer 6

the 1/2 and the 2 cancel out in front of log y, and the first 1/2 comes from the sqrt(10).

Answer 7

Oh ok i get it. the 2 and the ½ not being in front of the log y was throwing me off. thank you!

Answer 8

So do you understand where the first 1/2 comes from?

Answer 9

yes its for the square root. i was also wondering if you can help me with another problem? i posted it a while ago but only one person replied and they were unsure about the calculator part

Answer 10

sure

Answer 11

solve the inequality ln x ≤.8^x using your calculator.

i've been putting in ln(x)-.8^x in my calculator.
i know the answer is (0,1.9188] but not sure how to get it

Answer 12

Let me think about this.

Answer 13

Are you supposed to do this with a graphic calculator?

Answer 14

yes i have a TI-84

Answer 15

Great, I do too. So first you plot the functions ln x and .8^x.

Answer 16

so put them in separately?

Answer 17

That's what I would do, but you can do ln x - 0.8^x too if you want.

Answer 18

If you do it my way you calculate the point where they intersect next, you'll get 1.9188.

If you do it with you one function you'll have the calculate the zero of that function, also 1.9188.

Answer 19

Then you just look in the plot where 0.8^x is bigger than ln x.

Answer 20

Or if you use ln x -0.8^x, where that function is negative.

Answer 21

sorry it took so long to respond…I'm at work.
but i know how to graph it i just get stuck when it comes time to look for the point.

Answer 22

I'll take you through the steps, are you using two functions or only ln x -0.8^x ?

Answer 23

I'm using ln x -0.8^x

Answer 24

Ok, first thing you might want to do is change your window settings, so you can see what's going on. I'm using xmin=0, xmax=10, ymin=-2, ymax=2.

Answer 25

ok got that

Answer 26

To calculate the zero: Go to calc menu (2nd + trace) and select zero. You'll see a cursor in the plot and it's asking for the left bound, so move the cursor left of the zero. Press enter. It'll ask for the right bound, so move the cursor right of the zero. Finally it'll ask for a guess, this isn't really important, just move you cursor somewhere close to the zero. Press enter. You'll get the answer.

Answer 27

this is where i always get stuck so i do move it left of the zero and then when you say move it to the right i don't move it very much right? when i press enter at the last step it says error

Answer 28

What error do you get? No sign change?

Answer 29

i just did it again and i got it! thank you so much. I think before i pressed enter without moving it

Answer 30

great

Answer 31

so on my calc it says x=1.9188 y=0 but the answer i am supposed to get is (0, 1.9188] does that just mean they graphed it different? but my answer is still correct?

Answer 32

At this point you've only calculated the zero of lnx -0.8^x, the x for which ln x =0.8^x. The question was to solve the inequality ln x ≤.8^x, so you'll need to find the values of x for which 0.8^x is bigger than ln x. From the plot you can see that that's the case for the x left of the zero, so the answer is (0,1.9].

Answer 33

We can't have negative values of x, because of the logarithm, that's where the zero comes from.

Answer 34

oh ok i get it now. thanks again for your help!

Answer 35

great, no problem.