# Math Help - Solve for X in equations

1. ## Solve for X in equations

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

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

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

then:

$5x = 2.6 \ln(46.38)$

so:

$x=0.52~ \ln(46.38)$

RonL

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

Multiply through by $e^x$

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

so:

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

then let $y=e^x$ so:

$
y^2-4y-1=0
$

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

RonL