Question

Express the following in terms of log x and y \[log_3(\frac{x^2sqrt[3]{x-2}}{(2x+3)^5})\]

Answer 1

I got \[2log_3(x)+\frac{1}{3}log_3(x-2)-5log_3(2x+3)\] but is that what they asked for? in terms of x and y?

Answer 2

Write the question using equation editor..

Answer 3

Oh sorry..

Answer 4

@waterineyes \[\log_3(\frac{(x^2\sqrt[3]{x-2})}{(2x+3)^5})\]

Answer 5

You have very right till here but like you, I also did not get the question what it is asking about?

Answer 6

Where did you read this question can you attach that page here?

Answer 7

On a past final and no I am not able to... I don't have a scanner... but I double checked and those are the exact instructions and that is the question...

Answer 8

u got it right but what is y?!!

Answer 9

I don't know... I thought you guys may have seen these instructions before and recognize what to do...

Answer 10

So you need to use some properties of log
Which law are you having trouble with?

Answer 11

\[\log_3(\frac{(x^2\sqrt[3]{x-2})}{(2x+3)^5}) \]

You have division in there so why don't you first use \[\log_3(\frac{u}{v})=\log_3(u)-\log_3(v)\]

Answer 12

Is my answer directly at the top correct @myininaya?

Answer 13

It is correct if you are writing in terms of \[\log_3(x) \text{ and } \log_3(y)\]
It seems though your directions say log(x) and log(y)

Answer 14

If so you have just a little more work

Answer 15

But what you have so far is correct! :)

Answer 16

So what do I do to get it to where it needs to be? :)

Answer 17

Recall the change of base formula:
\[\log_3(u)=\frac{\ln(u)}{\ln(3)}=\frac{\ln(10)}{\ln(10)} \cdot \frac{\ln(u)}{\ln(3)}=\frac{\ln(10)}{\ln(3)} \frac{\ln(u)}{\ln(10)}\]
\[=\log_3(10) \cdot \log_{10}(u) =\log_3(10)\log(u) \text{ note: }\log_{10}(u)=\log(u) \]

Answer 18

Okay...

Answer 19

Okay...I still don't know what to do..

Answer 20

Well I'm reading the instructions and it seems like it wants the parts containing the variables to be base 10

Answer 21

And I see no y
Did you mean to write a y there?

Answer 22

What exactly do you instructions say?

Answer 23

Express the following in terms of logarithms of x and y

Answer 24

You know you have no y up there right?

Answer 25

Yes... there is no y on my question either that's why I am so confused...

Answer 26

But anyways it looks like you want the part containing the variable part to be base 10
that is why i was using change of base

Answer 27

Well, we didn't learn the change base formula at all so I guess it is not required for me to go any further from my answer... Thanks so much for all your help everyone!