Question

Write the equation ${\log }_{36}\left(6\right)=\frac{1}{2}$ in exponential form.

Short answer

The required exponential form is $6={36}^{\frac{1}{2}}$.

Step-by-step solution

Step 1. Write down the given equation.

The given logarithmic equation is ${\log }_{36}\left(6\right)=\frac{1}{2}$.

Step 2. Converting logarithmic equation to exponential form.

The exponential form of ${\log }_{36}\left(6\right)=\frac{1}{2}$is written as:

$\begin{array}{l}{\log }_{36}\left(6\right)=\frac{1}{2}\mathrm{....}\left(\text{Given}\right)\\ 6={\left(36\right)}^{\frac{1}{2}}\mathrm{....}\left(\begin{array}{l}\text{Applyexponential}\\ \text{form}\end{array}\right)\\ 6={36}^{\frac{1}{2}}\end{array}$

Step 3. Conclusion.

The required exponential form is $6={36}^{\frac{1}{2}}$.