How do you solve $5 \cdot e^{2 n} = 56.7$ $5*e^(2n)=56.7$ ?

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How do you solve $5 \cdot e^{2 n} = 56.7$ $5*e^(2n)=56.7$ ?

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Answer 1 · 2017-06-26T15:24:02

I got: $n = \frac{1}{2} ln (11.34) = 1.214168$ $n=1/2ln(11.34)=1.214168$

Explanation:

We can rearrange it:
$e^{2 n} = \frac{56.7}{5}$ $e^(2n)=56.7/5$
$e^{2 n} = 11.34$ $e^(2n)=11.34$
apply the natural log to both sides:
$ln [e^{2 n}] = ln (11.34)$ $ln[e^(2n)]=ln(11.34)$
use a property of logs:
$2 n ln (e) = ln (11.34)$ $2nln(e)=ln(11.34)$
and then:
$2 n = ln (11.34)$ $2n=ln(11.34)$
$n = \frac{1}{2} ln (11.34) = 1.214168$ $n=1/2ln(11.34)=1.214168$

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How do you solve $5 \cdot e^{2 n} = 56.7$ $5*e^(2n)=56.7$ ?

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