Question

Use the propties of logarithms to expand

Answer 1

\[\ln (\sqrt{a(b ^{3}+c ^{5})})\]

Answer 2

log(ab) = log(a) + log(b)
log(a/b) = loga - log(b)
log(a^b) = blog(a)

note that sqrt(x) = x^(1/2)

Answer 3

@Euler271 sooo \[\ln (a(b ^{3}+c ^{5})^{\frac{ 1 }{ 2 }}\]

Answer 4

yes

Answer 5

they are both ^1/2 though

Answer 6

I know I'm going to use the 1st log rule but I don't know where to start

Answer 7

the ln is also ^1/2 ?

Answer 8

oh i'm sorry, the a!

Answer 9

\[\ln([a(b^3 + c^5)]^\frac{ 1 }{ 2 })\]

Answer 10

i'd start like this:

\[\frac{ 1 }{ 2 } \ln(a(b^3 + c^5))\]

then i'd use the first one

Answer 11

im leaving for a while so i'll leave my answer:

\[\frac{ 1 }{ 2 }\left( \ln(a) + \ln(b^3 + c^5) \right)\]

Answer 12

ok, thanks!