How do you condense 3 ln 6 + 3 lnx?

Apr 4, 2016

Answer:

$3 \ln \left(6\right) + 3 \ln \left(x\right) = \ln \left(216 {x}^{3}\right)$

Explanation:

We will use the following properties:

• $\ln \left(a\right) + \ln \left(b\right) = \ln \left(a b\right)$
• $x \ln \left(a\right) = \ln \left({x}^{a}\right)$

With those, we have

$3 \ln \left(6\right) + 3 \ln \left(x\right) = 3 \left(\ln \left(6\right) + \ln \left(x\right)\right)$

$= 3 \ln \left(6 x\right)$

$= \ln \left({\left(6 x\right)}^{3}\right)$

$= \ln \left(216 {x}^{3}\right)$