a quick question about working with logs

is this true?

ln(x) + ln(y) = ln(x + y)

Question

a quick question about working with logs

is this true?

ln(x) + ln(y) = ln(x + y)

agent0smith · Answer

No. loga+logb = logab

isaiah.feynman · Answer

$$\ln (a)+\ln (b)=\ln (ab)$$

anonymous · Answer

so if I have ln(x +y), is there any way to simplify that, or do I just work with it as it is?

isaiah.feynman · Answer

Yes. For example if you have $$\ln (5+9) $$ that equals $$\ln (14)$$. But if you have $$\ln (5)+\ln (9)$$ that equals $$\ln (5\times9) = \ln (45)$$

anonymous · Answer

ok, that makes sense, thank you.  I'm actually working on differentation and forgot the log rules.  what I actually have is ln(x^2 + x + 1) so I was looking for the rule that would apply.  Since I don't know the value of my x I'll leave it as it is or use substitution.  Thank you.

isaiah.feynman · Answer

Wait are you trying to differentiate that function?

anonymous · Answer

it's using logaritmic differentiaton to find the derivitive.  I"m using the online derivative calculator, but making sure I understand all the steps too.  I"m sort of taking calc 2 10 years after I took calc 1.  Having some difficutlies

anonymous · Answer

my internet is cutting in and out so I'll keep plugging away at it

isaiah.feynman · Answer

See. $$f(x)=\ln (x^{2}+x+1)$$$$f \prime(x)=\frac{ 1 }{ x^{2}+x+1 }\times(x^{2}+x+1)\prime $$

anonymous · Answer

Chain rule!!! I am getting some of it.  thank you

agent0smith · Answer

Derivative of ln(f(x)) is $$\Large \frac{ f'(x) }{ f(x)}$$ or the derivative of the function insde the log, divided by the function inside the log