ln x = 1/3 (ln 16 + 2ln2)

Question

anonymous · Answer

4

anonymous · Answer

ln16+2ln2 --> ln16 +ln2^2 -> ln16+ln4 -> ln16*4
$$ e^{lnx} = (1/3)ln(16*4)$$
$$x=54e^{1/3}$$

anonymous · Answer

$$x=64e^{1/3}$$

anonymous · Answer

That's wrong, the answer is 4.

anonymous · Answer

Are you able to show me the work?

anonymous · Answer

One sec

anonymous · Answer

Google Chrome just crashed my openstudy Tab, oh lord.

anonymous · Answer

All that writing for naught.

anonymous · Answer

Essentially, you need two properties of logarithms:
$$1.\log(a)+\log(b)=\log(a*b)$$
$$2.b\log(a)=\log(a^b)$$
 See if you can work with that.

anonymous · Answer

Oh man :(. I just dont think I am writing it correctly and wanted to see how did you solve it

anonymous · Answer

so combine those two logarithms on the right to get $$log(16*4)$$, which is $$log(4^3)$$ and then use property "2" to get rid of that third power.

anonymous · Answer

What's property 2?

anonymous · Answer

The second thing I list in a previous post, scroll up.

anonymous · Answer

the answer is 4, correct

anonymous · Answer

I hate google chrome now.

anonymous · Answer

I'm sorry to bother you, but I'm just so confused. What about the 1/3?

anonymous · Answer

Well, now you have $$\frac{1}{3}\log(4^3)$$ using that second property the coefficient in front of  natural log becomes the power of 16, so $$\log(4^{3\frac{1}{3}})=\log(4)$$

anonymous · Answer

power of $$4^3$$ not 16.

Typo.

anonymous · Answer

thanks again! sorry about your computer problems :/