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:

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

Step 3. Verify the result for obtained value.

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

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

Similarly, for $x = 5$ ,

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

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

Step 4. Conclusion.

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

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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.

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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

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

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