Question

Solve the equation $5^{n-3}=\frac{1}{25}$. Check your solution.

Short answer

The solution for the equation is$n=1$.

Step-by-step solution

Step 1. Write down the given equation.

The given equation is $5^{n-3}=\frac{1}{25}$.

Step 2. Simplify the equation.

The given equation $5^{n-3}=\frac{1}{25}$is solved as:

$\begin{array}{l}{5}^{n-3}=\frac{1}{25}\mathrm{....}\left(\text{Given}\right)\\ 5^{n-3}=\frac{1}{{\left(5\right)}^2}\\ 5^{n-3}={\left(5\right)}^{-2}\\ n-3=-2\\ n=1\end{array}$

Step 3. Verify the result for obtained value.

Plugging $n=1$in given equation and verify the result.

$\begin{array}{l}{5}^{n-3}=\frac{1}{25}\mathrm{....}\left(\text{Given}\right)\\ 5^{\left(1\right)-3}=\frac{1}{25}\\ 5^{-2}=\frac{1}{25}\\ \frac{1}{5^2}=\frac{1}{25}\mathrm{....}\left(\text{True}\right)\end{array}$

Hence the solution is verified for $n=1$.

Step 4. Conclusion.

The solution for the given equation is $n=1$.