Solve for X in equations

**oldschool999** · August 4th 2007, 02:29 AM

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

**CaptainBlack** · August 4th 2007, 02:45 AM

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

**CaptainBlack** · August 4th 2007, 02:51 AM

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:

$<br /> y^2-4y-1=0<br />$

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

Thread: Solve for X in equations

LinkBack

Thread Tools

Display

Solve for X in equations

Similar Math Help Forum Discussions

How should I solve these equations?

Solve the following equations for 0<x<360 ?

solve the equations

May someone solve this equations for me?

Solve the following equations

Search Tags