condense the logarithms expression

[puzzled01]

ln(x+4)-3ln x-ln y

I know x+4 cannot be reduced and - means divide but I am totally confused.
Does anyone know any tricks to remember this stuff? :x

 

[jonboy]

You just got to know your rules. That's the only trick I use.

As for \(\displaystyle \L \;ln(x+4)\,-\,3ln\,x\,-\,ln\;y\)

Recall log rule three here.

So what do you think you can do with the \(\displaystyle 3ln\,x\) ?

 

[puzzled01]

do I + (x)^-3 ?

 

[jonboy]

do I + (x)^-3 ?

Good try.

You make the \(\displaystyle \;\,-\,3ln\,x\,\Rightarrow\,\,-\,ln\,x^3\)

Just leave the negative sign in front of the \(\displaystyle ln\) . It's the same as: \(\displaystyle \L \;\,-\,+\,3ln\,x\;\Rightarrow\;-\,lnx^3\)

 

[puzzled01]

do I the -y ?
After that I'm lost.

 

[jonboy]

do I the -y ?
After that I'm lost.

No. If there's just an understood one in front of the y it's pointless to move it. Simplifying 3lnx is all you can do.

BTW here shows 4 common log mistake, you should check it out so you don't do them.

 

[Mrspi]

ln(x+4)-3ln x-ln y

I know x+4 cannot be reduced and - means divide but I am totally confused.
Does anyone know any tricks to remember this stuff? :x

"tricks" are something grade-school kids look for.

There are only THREE basic rules for logs......shouldn't be too hard to memorize them.

log ab = log a + log b

log a/b = log a - log b

log a^m = m log a

The same rules apply for natural logs.....

 

[puzzled01]

If something makes it easier for me to remember I'm going to use it no matter how old I am!

 

[Mrspi]

If something makes it easier for me to remember I'm going to use it no matter how old I am!

Ok....but if there were some neat "trick" you could use, I'd think someone would have mentioned it by now. And no one did. Thus, your best bet is to take the time you've spent waiting for a "trick" and use it to memorize those three rules.

 

[pka]

ln(x+4)-3ln x-ln y
Does anyone know any tricks to remember this stuff?

Work at least twenty-five such problems. Make sure you have the answers so you can check your work.
\(\displaystyle \L \ln (x + 4) - 3\ln (x) - \ln (y) = \ln \left( {\frac{{x + 4}}{{x^3 y}}} \right)\)