Chapter 10: Q. 108 (page 1019)

In the following exercises, solve each equation.
$\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$

Short Answer

Expert verified

The answer is $x = - 1, x = 3$

Step by step solution

Step 1. Given

The equation is $\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$

Step 2. Solve the equation

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

Bases are same so the exponents should be equal.

$x^{2} - 3 = 2 x x^{2} - 2 x - 3 = 0 x^{2} - 3 x + x - 3 = 0 x (x - 3) + 1 (x - 3) = 0 (x - 3) (x + 1) = 0$

So,

$x = 3 x = - 1$

Step 3. Check the answers

Put $x = 3$ in given equation,

$\frac{e^{x^{2}}}{e^{3}} = e^{2 x} \frac{e^{{(3)}^{2}}}{e^{3}} = e^{2 (3)} \frac{e^{9}}{e^{3}} = e^{6} e^{9 - 3} = e^{6} e^{6} = e^{6}$

True

Put $x = - 1$ in given equation,

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

True

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In the following exercises, solve each equation.
$\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equation

Step 3. Check the answers

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In the following exercises, solve each equation.ex2e3=e2x

Short Answer

Step by step solution

Step 1. Given

Step 2. Solve the equation

Step 3. Check the answers

One App. One Place for Learning.

Most popular questions from this chapter

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In the following exercises, solve each equation.
$\frac{e^{x^{2}}}{e^{3}} = e^{2 x}$