Help with logs

- brandonw998

Help with logs

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- brandonw998

##### 1 Attachment

- brandonw998

I'm not sure how to plug in the numbers, even in Mathway I couldn't get it to work

- WolframWizard

Use logarithmic rules to pull apart each expression. For a) use the sum and difference rules of logs to pull apart the expression into ln(a^-2)-ln(b)-ln(c). Then use the power rule to pull out the exponent. -2ln(a)-ln(b)-ln(c). Now you can plug in the values given for ln(a), ln(b), and ln(c). It will be -2(2)-3-5 which is -12. Try this for the rest of the problems.

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## More answers

- brandonw998

Ohh I see! I'll try that

- amoodarya

\[\ln a^m=m lna\] for example
\[\ln \sqrt{b^2c^{-3}a^{-4}}=\frac{ 1 }{ 2 } \ln b^2c^{-3}a^{-4}=\\\frac{ 1 }{ 2 }( \ln b^2+\ln c^{-3}+\ln a^{-4})=\\\frac{ 1 }{ 2 } (2\ln b-3lnc-4lna)\]

- brandonw998

Is part b -6.5?

- brandonw998

Sorry, it's -8.5?

- brandonw998

Part C is 5.67?

- WolframWizard

Yes -8.5 is correct.

- brandonw998

Part D is a little confusing, is it -10?

- brandonw998

I got Part C and D wrong I'll try again

- brandonw998

I need help with Part C and D

- WolframWizard

Part C is either (lna+3lnb)*(lnb+lnc)^2 or (lna+3lnb)/(-2(lnb+lnc)). I'm not sure exactly what part of the expression the -2 exponent belongs to. Part C is either 704 or -.6875.
Part D is -2lnc*(lna-lnb)^3 which is +10 because it is the same as (-10)*(-1)^3.

- mathmale

The trick here is to apply rules of logs before substituting in the given values for log a, log b, log c, and so on.
Part D involves multiplication. What is the log of E * F, in terms of log E and log F?
What is\[\ln c ^{-2}\]

- mathmale

in terms of ln c?

- mathmale

Which rule of logs applies to division? How would you simplify \[\ln \frac{ P }{ Q }?\]

- mathmale

Hope this helps you to get back on track.

- brandonw998

.04?

- mathmale

I've asked a lot of questions. Which one were you answering here?

- brandonw998

The lnc^-2

- mathmale

Actually, Brandon, I'd wanted y ou to use rules of logs FIRST, and only after having simplified ln c^(-2) as far as possible, substitute ln c = 5. Mind doing that now?
Using rules of logs, simplify ln c^(-2)

- mathmale

Brandon?

- brandonw998

I am having a little trouble, most of this is new to me

- mathmale

do you have access to a list of rules of logarithms? If not, good idea to make one up.
You are to simplify \[\ln c ^{-2}\]

- mathmale

The rule for simplifying powers of c is as follows:

- mathmale

\[\ln c^d=d*\ln c\]

- mathmale

Following this rule, simplify:\[\ln c ^{-2}\]

- mathmale

Brandon, what's the value of "d" in this problem?

- brandonw998

-2?

- brandonw998

-2 * lnc

- mathmale

That's right! Now, go back to the original problem. It tells us that ln c is what?
Please write ln c, not lnc.
ln c = ?

- brandonw998

5

- mathmale

Right. Therefore, \[\ln c ^{-2},when \ln.c=5, is -2 (5)=?\]

- brandonw998

-10

- brandonw998

oh so it is not 5^-2

- brandonw998

That's a part that was confusing me

- mathmale

-10 is correct. 5^-2 is not.

- mathmale

|dw:1449446735321:dw|

- mathmale

Goes to show why it is important to list, study, apply and review rules of logs.

- brandonw998

Yes I definitely need to study the laws and rules more

- mathmale

|dw:1449446835362:dw|

- mathmale

|dw:1449446905494:dw|

- mathmale

|dw:1449446974429:dw|

- mathmale

Poke, poke. Brandon, where are you?

- brandonw998

Is it -0.0666?

- mathmale

I'm most interested in seeing how you arrive at an answer than I am in the answer itself.
Please apply the rules of logs I've reviewed for you to simplify |dw:1449447449454:dw|

- mathmale

No typo here. Problem gave you b^1; I gave you just b. Note that ln b^1 = lin b = 3

- mathmale

Hint: Hold that exponent 3 for last!!

- brandonw998

2/3=0.666^3=.29629?

- mathmale

You substituted the values for ln a and ln b before you applied the rules of logs.

- mathmale

a/b is a quotient. What is the rule of logs for ln a/b?

- mathmale

Do not substitute the values of ln a and ln b until after you've applied the rule of logs for quotients.

- brandonw998

2-3=-1

- brandonw998

-1^3=-1

- mathmale

Here's what I was hoping you would do:

- mathmale

Just a moment; I made a mistake and have to correct it.

- mathmale

|dw:1449448077401:dw|

- brandonw998

It's -1 correct?

- mathmale

|dw:1449448231446:dw|

- mathmale

But yes, your -1 is correct. Congrats!

- mathmale

You got these results 9-10 minutes ago, but I didn't know where they came from. Sorry to make you jump thru hoops, but ...

- brandonw998

|dw:1449448375250:dw|

- mathmale

|dw:1449448419163:dw|

- mathmale

So, for (d), we get ln c^(-2) - 1, right? Go back and find our answer for ln c^(-2).

- mathmale

Brandon, I need to move on; been on the computer most of the afternoon.
Now you know my user name (mathmale) in case you'd like to work with me again.
Best of luck to you.

- brandonw998

Thank you so much. I'm sorry I'm a little slow at this. I will get better soon!

- mathmale

Very happy to work with you. Bye for now!

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