Chapter 10: Q. 10.30 (page 1015)

Solve:
$\frac{e^{x^{2}}}{e^{x}} = 6$

Short Answer

Expert verified

By solving $\frac{e^{x^{2}}}{e^{x}} = 6$ , the value of $x$ is $- 2, 3$

Step by step solution

Step 1. Given

An expression $\frac{e^{x^{2}}}{e^{x}} = 6$

To solve the expression.

Step 2. Use the property of exponent

By using the property of exponent, $\frac{a^{m}}{a^{n}} = a^{m - n}$ ,

$e^{x^{2} - x} = 6$

Step 3. Write a new equation by setting the exponents equal.

Since the bases are same, the exponents must be equal.

$x^{2} - x = 6 x^{2} - x - 6 = 0 x^{2} - 3 x + 2 x - 6 = 0 (x - 3) (x + 2) = 0 x = - 2, 3$

The value of $x$ is $- 2, 3$

Step 4. Check the solutions.

When $x = - 2$ ,

$\frac{e^{{(- 2)}^{2}}}{e^{- 2}} = e^{6} \frac{e^{4}}{e^{- 2}} = e^{6} e^{4 + 2} = e^{6} e^{6} = e^{6}$

When $x = 3$ ,

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

Hence the solution has been checked.

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Solve:
$\frac{e^{x^{2}}}{e^{x}} = 6$

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the property of exponent

Step 3. Write a new equation by setting the exponents equal.

Step 4. Check the solutions.

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Solve:ex2ex=6

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the property of exponent

Step 3. Write a new equation by setting the exponents equal.

Step 4. Check the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Mechanics Maths

Geometry

Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve:
$\frac{e^{x^{2}}}{e^{x}} = 6$