Question

Which of the following is the simplified version of 1/2 log 3 x + 2 log 3 y – 4 log 3 z ?

Answer 1

\[\frac{ 1 }{ 2 } \log _{3} x+2 \log _{3} y-4\]

Answer 2

i assume you'll post choices ?
and the expression is \(\large \frac{ 1 }{ 2 } \log _{3} x+2 \log _{3} y-4\log_3z\)
right ?

Answer 3

log 3 sqrt(x) / y^2z^4

log 3 sqrt(xy^2) / z^4

log 3 sqrt(xz^4) / y^2

log 3 x3yz

Answer 4

\[\log_{3}(\sqrt{x}y^2)/z^4\]

Answer 5

ok, we will use these properties,
\(a \log b = \log b^a \)
\(\log a +\log b = \log ab\)
\(\log a -\log b = \log a/b\)
heard of them ?

Answer 6

yes @hartnn

Answer 7

so, which one will u use for 1/2 log x ?? (forget about the 3 as of now)

Answer 8

the middle one ?

Answer 9

nopes,
\(a \log b =\log b^a\)
\((1/2)\log x = .... ?\)

Answer 10

oh okay

Answer 11

i was asking what will 1/2 log x simplify to ?

Answer 12

log x ^1/2

Answer 13

correct!
in same way, what about 2 log y =... ?

Answer 14

and 4 log z = ... ?

Answer 15

log y ^2
log z ^4

Answer 16

good good!
now we will use other properties,

log a + log b = log ab
log (x^1/2) + log y^2 = ... ?

Answer 17

log x^1/2y^2

Answer 18

correct,
log a - log b = log a/b
so,
log (x^1/2y^2 ) - log z^4 = ... ?

Answer 19

log 3 (x^1/2y^2) / z^4

Answer 20

good work, thats your answer :)

Answer 21

las thing, x^1/2 = sqrt x

Answer 22

thank youu (:

Answer 23

welcome ^_^