Help With Log Notation

**mathguy20** · May 2nd 2011, 04:05 PM

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

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

Thanks!

**e^(i*pi)** · May 2nd 2011, 04:06 PM

$\ln(x) = \log_e(x)$

**mathguy20** · May 2nd 2011, 04:12 PM

Thanks for the quick response! Does $e$ = 10 is the base if it not stated, just like normal logs?

**e^(i*pi)** · May 2nd 2011, 04:17 PM

Originally Posted by mathguy20

Thanks for the quick response! Does $e$ = 10 is the base if it not stated, just like normal logs?

$e \neq 10$ under any circumstance. In general however: $\ln(x) = \log_e(x)$ and $\log(x) = \log_{10}(x)$ where the base isn't explicitly stated

**mathguy20** · May 2nd 2011, 04:20 PM

Got it -- here's another log question if you don't mind.

How would I solve for x?

$2log_4(x) - log_4(x+3) = 1$

**Quacky** · May 2nd 2011, 04:27 PM

We have: $Log_4{(x^2)}-Log_4{(x+3)}=1$

Can you see why?

So combine logs using the $Log(a)-Log(b)=Log(\frac{a}{b})$ and see if you get anywhere.

**mathguy20** · May 2nd 2011, 04:36 PM

Yeah - so would it be $Log_4(\frac {x^2}{x+3}) = 1$ ?

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 $4 = \frac{x^2}{x+3}$ . So $x = {-2, 6}$ ?

**Quacky** · May 2nd 2011, 04:41 PM

Originally Posted by mathguy20

Yeah - so would it be $Log_4(\frac {x^2}{x+3}) = 1$ ?

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 $4 = \frac{x^2}{x+3}$ . So $x = {-2, 6}$ ?

Yeah. Remember that you can always try it and substitute your answer into the original equation to check!

Edit: although x can't be -2 because this isn't defined by your original equation. Be careful with logs; this happens frequently!

**mathguy20** · May 2nd 2011, 04:43 PM

Originally Posted by Quacky

Yeah. Remember that you can always try it and substitute your answer into the original equation to check!

I see how I can plug in -2 and 6 to the equation we got in the final steps, but is there a way I can plug that into the original equation and check it on my TI-84? (I'm not sure how to use bases other than 10 on the calculator.)

**Quacky** · May 2nd 2011, 04:48 PM

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.

**bjhopper** · May 2nd 2011, 07:12 PM

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

Thread: Help With Log Notation

LinkBack

Thread Tools

Display

Help With Log Notation

Similar Math Help Forum Discussions

What does this notation mean? Leibniz's notation for second derivative?

nCr notation

Notation

Absolute Value Notation/Inequality and Interval Notation

Notation