Question

Write the equation ${\log }_3\left(81\right)=4$ in exponential form.

Short answer

The required exponential form is $81=3^4$.

Step-by-step solution

Step 1. Write down the given equation.

The given logarithmic equation is ${\log }_3\left(81\right)=4$.

Step 2. Converting logarithmic equation to exponential form.

The exponential form of ${\log }_3\left(81\right)=4$is written as:

$\begin{array}{l}{\log }_3\left(81\right)=\mathrm{4....}\left(\text{Given}\right)\\ 81={\left(3\right)}^4\mathrm{....}\left(\begin{array}{l}\text{Applyexponential}\\ \text{form}\end{array}\right)\\ 81=3^4\end{array}$

Step 3. Conclusion.

The required exponential form is $81=3^4$.