Thread: 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

What base are you working in?

That's exactly how the problem appears. I guess just the assumed bases of e and 10.

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.

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"?

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

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

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

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

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

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

Originally Posted by colby2152

log notation usually means base ten

My bad.

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.

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.