Could anyone help me with Natural Logarithms?

Question

nicole143 · Answer

@campbell_st

campbell_st · Answer

well it depends on the question...

nicole143 · Answer

Okay, I have to solve: 2 In x + 3 In 2 = 5

anonymous · Answer

Naturally. Start with 
2 ln x = ln (x^2) 
3 ln (2) = ln(2^3) = ln(8)

because c ln(d) = ln(d^c), 

now also 
note that ln(A) + ln(B) = ln(AB) 
so your first two expressions become ln(8 x^2) = 5

now go from ln to exp 
8 x^2 = exp(5)

and solve this by getting x = etc.

nicole143 · Answer

Thank you, I think I get it now(: @douglaswinslowcooper

nicole143 · Answer

Will you be on here for a bit longer? I could use some help on a few others? @douglaswinslowcooper

anonymous · Answer

I was heading for bed. Let's try one or two, anyway.

nicole143 · Answer

Okay, thank you! I have to find the annual interest rate when the initial investment is $350 and is worth $429.20 after being continuously compounded for 6 years. I know most of how to do the problem I just need the equation to be able to work it backwards..

anonymous · Answer

OK. Continuous compounding means 
A = P exp(k t),  where A is the final amount, P is the principle, t is the time and k is a rate constant.

A = 429.20 = (350) exp (6 k)

exp (6k) = (429.20)/9350)  = 1.226

take ln of both sides

6k = ln(1.226) = 0.204

k = 0.034 = 3.4%  per year, compounded continuously

rough check 350 (1.034)^6 = 427.75, just a little less because the compounding was only yearly rather than continuously.

Clear?

nicole143 · Answer

Let me work it out and see if I get it.

anonymous · Answer

Fine. I think you will.
The principle is that continuous compounding at k per period give growth factor of A/P=exp(kt), where t is the number of such periods.

Good night and good luck.

nicole143 · Answer

Thank you! Have a good night as well(: