Question

Help with logs

Answer 1

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

Answer 2

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.

Answer 3

Ohh I see! I'll try that

Answer 4

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

Answer 5

Is part b -6.5?

Answer 6

Sorry, it's -8.5?

Answer 7

Part C is 5.67?

Answer 8

Yes -8.5 is correct.

Answer 9

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

Answer 10

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

Answer 11

I need help with Part C and D

Answer 12

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.

Answer 13

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\[\ln c ^{-2}\]

Answer 14

in terms of ln c?

Answer 15

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

Answer 16

Hope this helps you to get back on track.

Answer 17

.04?

Answer 18

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

Answer 19

The lnc^-2

Answer 20

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)

Answer 21

Brandon?

Answer 22

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

Answer 23

do you have access to a list of rules of logarithms? If not, good idea to make one up.

You are to simplify \[\ln c ^{-2}\]

Answer 24

The rule for simplifying powers of c is as follows:

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

-2?

Answer 29

-2 * lnc

Answer 30

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 = ?

Answer 31

5

Answer 32

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

Answer 33

-10

Answer 34

oh so it is not 5^-2

Answer 35

That's a part that was confusing me

Answer 36

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