# Thread: Solve for X in equations

1. ## Solve for X in equations

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

2. Originally Posted by oldschool999
Solve for x in each equation. Question 1. $\displaystyle e^{5x} = 46.38^{(2.6)}$ Question 2. $\displaystyle e^x-e^{-x}=4$
1. Take natural logs:

$\displaystyle e^{5x} = 46.38^{(2.6)}$

then:

$\displaystyle 5x = 2.6 \ln(46.38)$

so:

$\displaystyle x=0.52~ \ln(46.38)$

RonL

3. Originally Posted by oldschool999
Solve for x in each equation. Question 1. $\displaystyle e^{5x} = 46.38^{(2.6)}$ Question 2. $\displaystyle e^x-e^{-x}=4$
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