# Combining log and ln?

• Jan 13th 2008, 12:47 PM
happydino1
Combining log and ln?
I have a problem about condensing logarithmic expressions with logs AND lns. Is this possible?

ln 5 + 3 ln 3 - log 4
• Jan 13th 2008, 12:52 PM
WWTL@WHL
What base are you working in?
• Jan 13th 2008, 12:54 PM
happydino1
That's exactly how the problem appears. I guess just the assumed bases of e and 10.
• Jan 13th 2008, 01:02 PM
WWTL@WHL
well $\displaystyle log_{e} x = lnx.$ In that case...

ln5 + 3ln3 - log4 = ln5 + ln3^3 - ln4
= ln5 + ln9 - ln4 = ln45 -ln4 = $\displaystyle ln \frac{45}{4}$

Hopefully someone will correct me if I'm wrong.
• Jan 13th 2008, 01:05 PM
colby2152
Quote:

Originally Posted by happydino1
I have a problem about condensing logarithmic expressions with logs AND lns. Is this possible?

ln 5 + 3 ln 3 - log 4

Why wouldn't this be "possible"?

$\displaystyle ln(5) + 3ln(3) - log(4)$

$\displaystyle ln(5*3^3) - log(4)$

$\displaystyle ln(135) - log_{10}(4)$

$\displaystyle ln(135) - \frac{ln(4)}{ln(10)}$

$\displaystyle ln(135) - \frac{ln(4)}{ln(10)}$
• Jan 13th 2008, 01:06 PM
colby2152
Quote:

Originally Posted by WWTL@WHL
well $\displaystyle log_{e} x = lnx.$ In that case...

ln5 + 3ln3 - log4 = ln5 + ln3^3 - ln4
= ln5 + ln9 - ln4 = ln45 -ln4 = $\displaystyle ln \frac{45}{4}$

Hopefully someone will correct me if I'm wrong.

log notation usually means base ten
• Jan 13th 2008, 01:13 PM
WWTL@WHL
Quote:

Originally Posted by colby2152
log notation usually means base ten

I read this on wiki: Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean loge(x) and got confused.

OP: Ignore my post.
• Jan 13th 2008, 01:53 PM
Krizalid
Quote:

Originally Posted by WWTL@WHL
I read this on wiki: Mathematicians, statisticians, and some engineers generally understand either "log(x)" or "ln(x)" to mean loge(x) and got confused.

Of course.

It's actually applied to integration and derivatives. (As far as I know.)

There're lots of calculus' books which use that.