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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 385 (page 1063)

In the following exercises, solve each equation.
$\frac{e^{x^{2}}}{e^{15}} = e^{2 x}$ .

Short Answer

Expert verified

The solution of the equation is $- 3$ and $5$ .

Step by step solution

01

Step 1. Given information.

The given equation is,

$\frac{e^{x^{2}}}{e^{15}} = e^{2 x}$ .

02

Step 2. Solving the equation.

Now to solve the equation we will write the same base on both sides of the equation and solve the obtained equation.

\frac{e^{x^{2}}}{e^{15}} = e^{2 x} e^{x^{2} - 15} = e^{2 x} x^{2} - 15 = 2 x x^{2} - 2 x - 15 = 0 (x - 5) (x + 3) = 0 x = - 3, 5

03

Step 3. Checking the result.

When $x = - 3$ ,

\frac{e^{{(- 3)}^{2}}}{e^{15}} = e^{2 (- 3)} e^{9 - 15} = e^{- 6} e^{- 6} = e^{- 6}

Therefore, this is true.

When $x = 5$ ,

$\frac{e^{{(5)}^{2}}}{e^{15}} = e^{2 (5)} e^{25 - 15} = e^{10} e^{10} = e^{10}$

Hence, this is true.

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Most popular questions from this chapter

In the following exercises, match the graphs to one of the following functions:

$鈸� 2^{x} 鈸� 2^{x + 1} 鈸� 2^{x - 1} 鈸� 2^{x} + 2 鈸� 2^{x} 鈭� 2 鈸� 3^{x}$

In the following exercises, find the inverse of each function.

$f (x) = - 2 x + 5$

In the following exercises, graph each exponential function:

$f (x) = 3^{x + 2}$

Convert from exponential to logarithmic form:

${(\frac{1}{3})}^{4} = \frac{1}{81}$ .

In the following exercises, solve each equation.

$e^{3 x} 路 e^{4} = e^{10}$

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