Question

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

Short answer

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

Step-by-step solution

Step 1. Write down the given equation.

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

Step 2. Simplify the equation.

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

$\begin{array}{l}{\left(\frac{1}{7}\right)}^{y-3}=\mathrm{343....}\left(\text{Given}\right)\\ {\left(7\right)}^{3-y}={\left(7\right)}^3\\ 3-y=3\\ y=0\end{array}$

Step 3. Verify the result for obtained value.

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

$\begin{array}{l}{\left(\frac{1}{7}\right)}^{y-3}=\mathrm{343....}\left(\text{Given}\right)\\ {\left(\frac{1}{7}\right)}^{\left(0\right)-3}=343\\ {\left(\frac{1}{7}\right)}^{-3}=343\\ 7^3=\mathrm{343....}\left(\text{True}\right)\end{array}$

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

Step 4. Conclusion.

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