Chapter 5: Q 100. (page 299)

Solve the equation.
$e^{- 2 x} = \frac{1}{3}$

Short Answer

Expert verified

The solution to the equation, $e^{- 2 x} = \frac{1}{3}$ is, $x = - \frac{1}{2} \ln \frac{1}{3}$ .

Step by step solution

Step 1. Given Information

The given equation to be solved is $e^{- 2 x} = \frac{1}{3}$ .

Step 2. Formula used

Natural logarithm:

$\ln e = 1$

Step 3. Finding Solution

The given equation is $e^{- 2 x} = \frac{1}{3}$ .

Take logarithm on both sides.

$\ln e^{- 2 x} = \ln \frac{1}{3} - 2 x \ln e = \ln \frac{1}{3} - 2 x = \ln \frac{1}{3} x = - \frac{1}{2} \ln \frac{1}{3}$

The solution to the given equationis, $x = - \frac{1}{2} \ln \frac{1}{3}$ .

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Solve the equation.
$e^{- 2 x} = \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Formula used

Step 3. Finding Solution

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Solve the equation.
$e^{- 2 x} = \frac{1}{3}$