# what's the difference between 2ln3 and 2ln(3)

• Aug 23rd 2011, 09:41 AM
StudentMCCS
what's the difference between 2ln3 and 2ln(3)
I have a problem, solve for x.

ln(x+2)-2ln(3)=0 ln(x+2)-2ln3=0

So I guess 2ln(3)=2ln

But first I did this because I didn't notice the second equation.

ln(x+2)=2ln(3)

[e^(2ln(3)]=x+2

x=[e^2ln(3)]-2

What do you think?
• Aug 23rd 2011, 09:50 AM
Siron
Re: what's the difference between 2ln3 and 2ln(3)
Your solution to solve $\displaystyle \ln(x+2)-2\ln(3)=0$ is fine, but you can simplify it this way:
$\displaystyle \ln(x+2)=2\ln(3)$
$\displaystyle \Leftrightarrow \ln(x+2)=\ln(9)$
and therefore
$\displaystyle x+2=9 \Leftrightarrow x=7$

Also notice: $\displaystyle e^{\ln(x)}=x$

But this statement:
$\displaystyle 2\ln(3)=2\ln$
doesn't make sense ... the two given equations are totally equal.
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