Question

Is this equation true? please help!

Answer 1

\[4 \log_{3} x+ \frac{ 1 }{ 2 } \log_{3} y-2 \log_{3}2= \log_{3} \frac{ x^4\sqrt{y} }{ z^2 }\]

Answer 2

it looks like you have a typo in the last term on the left side of the equal sign.

Answer 3

to find out, use the rules:
\[ \log(a\cdot b) = \log(a)+\log(b) \]
\[ \log(\frac{a}{ b}) = \log(a)-\log(b) \]
\[ \log(a^b) = b\log(a) \]

Answer 4

apply the rules to the right-hand side

Answer 5

what would be the a and the b?

Answer 6

match a and b to terms in the problem. For example you could say
a= x^4 sqrt(y) and b is z^2
now use the 2nd rule

Answer 7

what do you get if you match
a= x^4 sqrt(y) and b is z^2
and then use the 2nd rule
??

Answer 8

i really dont understand what the process is

Answer 9

The way to interpret this rule:
\[ \log(\frac{a}{ b}) = \log(a)-\log(b) \]
look at your problem
\[ \log(\frac{x^4 \sqrt{y}}{z^2}) \]
if you call all of the stuff in the top a and the stuff in the bottom b,
you can rewrite your problem as
log(a)- log(b) but replace a with "stuff in the top" and b with "stuff in the bottom"
can you do that?

Answer 10

\[\frac{ \log x^4\sqrt{y} }{ \log z^2}\]

Answer 11

there is NO RULE that says
\[ log\left( \frac{a}{b}\right) = \frac{log(a)}{log(b)}\]

Answer 12

which is what you did. you should use
\[ log\left(\frac{a}{b}\right) = log(a)- log(b) \]

Answer 13

the idea is you give the name "a" to the complicated \( x^4 \sqrt{y}\)
and the name "b" to \(z^2\)
the rule says
if you see a divided by b inside a log, like this
\[ log\left(\frac{a}{b}\right) \]
you can write it like this instead
\[ log(a)-log(b) \]
but you can replace the names "a" and "b" with the complicated stuff...

Answer 14

try again

Answer 15

\[\log x^4\sqrt{y} - \log z^2\]

Answer 16

yes. very good.

Answer 17

as practice, try using the 3rd rule
\[ \log(a^b) = b\log(a) \]
on the last term \(-\log(z^2) \)

Answer 18

I would let a be the name of z and b be the name of 2.