Question

I am trying to find the sums and differences of logarithms

Answer 1

do you have a specific problem?

Answer 2

\[\ln \sqrt[4]{ab ^{2}}\]

Answer 3

ahh..you know that \(\sqrt[4]{ab^3} \implies (ab^3)^{1/4}\) right?

Answer 4

yes. i just don't know what the final answer should look like.

Answer 5

so basically
\[\large \ln (\sqrt[4]{ab^3} \implies \ln (ab^3)^{1/4}\]
now i can use power rule
\[\large \frac{1}{4} \ln (ab^3)\]
now i apply the multiplication law of logarithms
\[\frac 14 \ln a + \frac14 \ln b^3\]
now i apply power rule again
\[\frac 14 \ln a + \frac 34 \ln b\]
do you get that?

Answer 6

I have \[ab^{1/2}\] but not sure where to go from there

Answer 7

oh wait..it's 2?? i thought it was 3

Answer 8

yes, its 2 :)

Answer 9

\[\large \ln (\sqrt[4]{ab^2}) = \ln (ab^2)^{1/4}\]
power rule
\[\large \frac 14 \ln (ab^2)\]
multiplication law
\[\frac14 \ln a + \frac 14 \ln b^2\]
power rule again
\[\frac 14 \ln a + \frac 24 \ln b\]
simplify
\[\frac 14 \ln a + \frac 12 \ln b\]
do you get that?

Answer 10

yes that is what i got

Answer 11

now, is there any more simplifying?

Answer 12

nope

Answer 13

ahh ok, i made it more complicated than it was. for some reason i was trying to cancel out ln to simplify

Answer 14

haha lol =))) your question was requiring sum of logarithms why cancel haha

Answer 15

yes, correct. lol thank you, may i ask another question?

Answer 16

sure shoot

Answer 17

ok i must graph this function: f(x)=log(x+1). I have worked out other similar functions where there is a number for the base. for example: \[\log _{2}(x+1)\]. I also know that log(x) is 10 but not sure if that is my base when using\[x=a^{y}\]

Answer 18

aww graphing :/ im weak in graphing

Answer 19

ok, lol. I actually have plugged in numbers and checked the graph, although the coordinates look a bit off and im just not certain they are correct.

Answer 20

would you know how to change log(x+1) into the \[x=a^{y}\] form?

Answer 21

yep... \(\log (x+1)\) has a base 10 so it's just like \(\log_{10} (x+1)\)
remember that if you see log and there's no base then it's automatic that it's 10

Answer 22

yes, i thought so. Just want sure. Ok so then it would be \[(x+1)=10^{y}\] correct?

Answer 23

if it was \[\log (x+1) = y\] then yes

Answer 24

thank you very much!!!

Answer 25

<tips hat>

Answer 26

:D