Question

3ln2 + 2ln4
write each as a single logarithm

Answer 1

Properties of logarithms!!!
\[\huge \ln x^p=p\ln x\]

Answer 2

I know the first thing I'm supposed to do is ln2^3+ln4^2 but then aren't you supposed to multiply them?

Answer 3

\(aln(b) = \ln(b)^a\) also, \(\ln(a)-\ln(b) = \ln \frac{ a }{ b }\) \(\ln(a)+\ln(b) = \ln(ab)\)

Answer 4

Later :)
\[\huge \ln2^3+\ln4^2=\ln8+\ln16\]And now use this property
\[\huge \ln(ab)=\ln(a)+\ln(b)\]

Answer 5

So is the answer 128?

Answer 6

No. Logarithms don't just suddenly disappear, silly ^.^

Answer 7

So how do I get the final answer?1

Answer 8

Well, using that property
\[\huge \ln(8)+\ln(16) = \ln(8\cdot 16)\]

Answer 9

I just did that! So \[\ln 128\]

Answer 10

Yeah, it's ln(128)
not just 128 :P

Answer 11

why does it say in my book that the answer is 7ln2 then?

Answer 12

Well, maybe you could use the fact that
\[\huge 128 = 2^7\]
and the first property I mentioned ^.^

Answer 13

Well that makes sense

Answer 14

I do love making sense ^.^

Answer 15

Another question I have is, 3ln5+4lnx

Answer 16

I solved it, I just want to know if I got the correct answer

Answer 17

Go for it :)

Answer 18

Okay I got \[\ln 125x ^{4}\]

Answer 19

Correct.

Answer 20

Ah thank you!