Question

expanding logs

Answer 1

condense \[1/3 logx-2\log(x+2)-4\log(y+2)\]

Answer 2

move the coefficients inside the logs
use the rule
\[ a \log(b) = \log(b^a) \]

Answer 3

does it matter if in base of three

Answer 4

no.

Answer 5

so log1/3x-2log2x+4-log4y+8

Answer 6

try again
the coefficient becomes an *exponent*
example: the first log becomes
\[ \log(x^\frac{1}{3}) \]

Answer 7

\[logx ^{1/3}-Log(x+2)^{2}-Log(y+2)^{4}\]
\
\

Answer 8

ok,
now if all the logs are the same base
you can use the rule
\[ \log(a) - \log(b)\ = \log(\frac{a}{b} )\]

Answer 9

but can i have loga-logb-logc= log a/b/c

Answer 10

the three logs are throwing me off

Answer 11

yes. a/b/c is the same as a/(b*c)

another way to do this is factor out the minus sign
\[ \log(x^(1/3) - (\log( (x+2)^2 ) +\log( (y+2)^4) )\]
and combine the logs inside the parens using log(a)+log(b)= log(a*b)

Answer 12

okso...