Q56. Solve the equation 49x=7x2-15. C... [FREE SOLUTION]

91影视

Chapter 10: Q56. (page 528)

Solve the equation $49^{x} = 7^{x^{2} - 15}$ . Check your solution.

Short Answer

Expert verified

The solution for the equation is $x = - 3, 5$ .

Step by step solution

Step 1. Write down the given equation.

The given equation is $49^{x} = 7^{x^{2} - 15}$ .

Step 2. Simplify the equation.

The given equation $49^{x} = 7^{x^{2} - 15}$ is solved as:

$\begin{array}{l} 49^{x} = 7^{x^{2} 鈭� 15} .... (Given) \\ {(7^{2})}^{x} = {(7)}^{x^{2} 鈭� 15} \\ {(7)}^{2 x} = {(7)}^{x^{2} 鈭� 15} \\ 2 x = x^{2} 鈭� 15 \\ x^{2} 鈭� 2 x 鈭� 15 = 0 \\ (x 鈭� 5) (x + 3) = 0 \\ x = 鈭� 3, 5 \end{array}$

Step 3. Verify the result for obtained value.

Plugging $x = - 3, 5$ in given equation and verify the result.

$\begin{array}{l} 49^{x} = 7^{x^{2} 鈭� 15} .... (Given) \\ 49^{(鈭� 3)} = 7^{{(鈭� 3)}^{2} 鈭� 15} .... (For x = 鈭� 3) \\ 49^{(鈭� 3)} = 7^{鈭� 6} \\ {(7^{2})}^{(鈭� 3)} = 7^{鈭� 6} \\ 7^{鈭� 6} = 7^{鈭� 6} .... (Truefor x = 鈭� 3) \end{array}$

Similarly, for $x = 5$ ,

$\begin{array}{l} 49^{x} = 7^{x^{2} 鈭� 15} .... (Given) \\ 49^{(5)} = 7^{{(5)}^{2} 鈭� 15} .... (For x = 5) \\ 49^{(5)} = 7^{10} \\ {(7^{2})}^{5} = 7^{10} \\ 7^{10} = 7^{10} .... (Truefor x = 5) \end{array}$

Hence the solution is verified for $x = - 3, 5$ .

Step 4. Conclusion.

The solution for the given equation is $x = - 3, 5$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve the equation $49^{x} = 7^{x^{2} - 15}$ . Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

91影视

Solve the equation 49x=7x2-15. Check your solution.

Short Answer

Step by step solution

Step 1. Write down the given equation.

Step 2. Simplify the equation.

Step 3. Verify the result for obtained value.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve the equation $49^{x} = 7^{x^{2} - 15}$ . Check your solution.