Solve for x in each equation. Question 1. $\displaystyle e^{5x} = 46.38^{(2.6)}$ Question 2. $\displaystyle e^x-e^{-x}=4$

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- Aug 4th 2007, 02:29 AMoldschool999Solve for X in equations
Solve for x in each equation. Question 1. $\displaystyle e^{5x} = 46.38^{(2.6)}$ Question 2. $\displaystyle e^x-e^{-x}=4$

- Aug 4th 2007, 02:45 AMCaptainBlack
- Aug 4th 2007, 02:51 AMCaptainBlack
Question 2:

Multiply through by $\displaystyle e^x$

$\displaystyle e^x-e^{-x}=4$

so:

$\displaystyle e^{2x}-1=4 e^x$

then let $\displaystyle y=e^x$ so:

$\displaystyle

y^2-4y-1=0

$

solving this gives $\displaystyle y=2 \pm \sqrt{5}$, but as $\displaystyle y>0$ only $\displaystyle y=2+\sqrt{5}$ is a valid solution if we want $\displaystyle x$ to be real. Then $\displaystyle x=\ln(2+\sqrt{5})$

RonL