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Chapter 10: Q50. (page 528)

Solve the equation ${(\frac{1}{7})}^{y - 3} = 343$ . Check your solution.

Short Answer

Expert verified

The solution for the equation is $y = 0$ .

Step by step solution

01

Step 1. Write down the given equation.

The given equation is ${(\frac{1}{7})}^{y - 3} = 343$ .

02

Step 2. Simplify the equation.

The given equation ${(\frac{1}{7})}^{y - 3} = 343$ is solved as:

$\begin{array}{l} {(\frac{1}{7})}^{y 鈭� 3} = 343.... (Given) \\ {(7)}^{3 鈭� y} = {(7)}^{3} \\ 3 鈭� y = 3 \\ y = 0 \end{array}$

03

Step 3. Verify the result for obtained value.

Plugging $y = 0$ in given equation and verify the result.

$\begin{array}{l} {(\frac{1}{7})}^{y 鈭� 3} = 343.... (Given) \\ {(\frac{1}{7})}^{(0) 鈭� 3} = 343 \\ {(\frac{1}{7})}^{鈭� 3} = 343 \\ 7^{3} = 343.... (True) \end{array}$

Hence, the solution is verified for $y = 0$ .

04

Step 4. Conclusion.

The solution for the given equation is $y = 0$ .

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