Question

Solve the equation $3^{n-2}=27$. Check your solution.

Short answer

The solution for the equation is $n=5$.

Step-by-step solution

Step 1. Write down the given expression.

The given equation is $3^{n-2}=27$.

Step 2. Simplify the equation.

The given equation $3^{n-2}=27$is solved as:

$\begin{array}{l}{3}^{n-2}=\mathrm{27....}\left(\text{Given}\right)\\ 3^{n-2}={\left(3\right)}^3\\ n-2=3\\ n=5\end{array}$

Step 3. Verify the result for obtained value.

Plugging $n=5$in given equation and verify the result.

$\begin{array}{l}{3}^{n-2}=\mathrm{27....}\left(\text{Given}\right)\\ 3^{\left(5\right)-2}=27\\ 3^3=\mathrm{27....}\left(\text{True}\right)\end{array}$

Hence the solution is verified for $n=5$.

Step 4. Conclusion.

The solution for the given equation is $n=5$.