What would $\displaystyle ln$ stand for in a log equation?

For example $\displaystyle 8ln x = 16$ ? Is that the same as $\displaystyle 8 log x = 16$ ?

Thanks!

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- May 2nd 2011, 04:05 PMmathguy20Help With Log Notation
What would $\displaystyle ln$ stand for in a log equation?

For example $\displaystyle 8ln x = 16$ ? Is that the same as $\displaystyle 8 log x = 16$ ?

Thanks! - May 2nd 2011, 04:06 PMe^(i*pi)
$\displaystyle \ln(x) = \log_e(x)$

- May 2nd 2011, 04:12 PMmathguy20
Thanks for the quick response! Does $\displaystyle e$ = 10 is the base if it not stated, just like normal logs?

- May 2nd 2011, 04:17 PMe^(i*pi)
- May 2nd 2011, 04:20 PMmathguy20
Got it -- here's another log question if you don't mind.

How would I solve for x?

$\displaystyle 2log_4(x) - log_4(x+3) = 1$ - May 2nd 2011, 04:27 PMQuacky
We have: $\displaystyle Log_4{(x^2)}-Log_4{(x+3)}=1$

Can you see why?

So combine logs using the $\displaystyle Log(a)-Log(b)=Log(\frac{a}{b})$ and see if you get anywhere. - May 2nd 2011, 04:36 PMmathguy20
Yeah - so would it be $\displaystyle Log_4(\frac {x^2}{x+3}) = 1$ ?

I think I got lost in the base 4, because I've only done those in base 10.

Then, I can just solve for x from $\displaystyle 4 = \frac{x^2}{x+3}$. So $\displaystyle x = {-2, 6}$ ? - May 2nd 2011, 04:41 PMQuacky
- May 2nd 2011, 04:43 PMmathguy20
- May 2nd 2011, 04:48 PMQuacky
I am unfamiliar with this exact calculator, but I would expect, if there isn't a button that calculates logs to all bases, that you can, using the change of base rule. If you convert the logs from base 4 to base 10, then you can plug the numbers in. I don't know whether there's a shorthand, my calculator can calculate logs to all bases for me so I don't have to worry.(Cool)

- May 2nd 2011, 07:12 PMbjhopper
Hello mathguy20,

log B4 (4) =1. Bring all terms to LHS.Combine all the log terms to 1 term= to 0.Solve for x

bjh