Question

Write expression as a single logarithm:
1/3 (lnx+lny)-4lnz
so... do I distribute the 1/3 first?

Answer 1

sounds fabulous to me

Answer 2

then use power rule for log

Answer 3

\[r \log_b(x)=\log_b(x^r)\]

Answer 4

then use product and quotient rule for log

Answer 5

properties of logarithms:
\[a \ln (b)=\ln (b ^{a})\]
\[\ln (a)+\ln (b)=\ln (ab)\]

Answer 6

And one more property:
\[\ln (a)-\ln (b)=\ln (\frac{ a }{ b })\]

Answer 7

1/3lnx+1/3lny= 1/3lnxy?

Answer 8

oh yeah you can do that :p

Answer 9

but you are still going to have to use power rule

Answer 10

@drayder It would probably be easier to start within the parentheses