# How do you write the equation 36^(3/2)=216 into logarithmic form?

${36}^{\frac{3}{2}} = 216 \iff {\log}_{36} \left(216\right) = \frac{3}{2}$

#### Explanation:

We can convert an exponential expression into a logarithmic one by this general formula:

${a}^{b} = c \iff {\log}_{a} \left(c\right) = b$

On the left, we can say that the number a, multiplied by itself b times, gives a result of c.

On the right, we can say that the number a, to achieve the number c, needs to be multiplied by itself b times.

We can therefore convert:

${36}^{\frac{3}{2}} = 216 \iff {\log}_{36} \left(216\right) = \frac{3}{2}$