Question

Write the equation $5^4=625$ in logarithmic form.

Short answer

The required logarithmic form is ${\log }_{5}625=4$.

Step-by-step solution

Step 1. Write down the given equation.

The given exponential equation is $5^4=625$.

Step 2. Converting exponential equation to logarithmic form.

The logarithmic form of $5^4=625$is written as:

$\begin{array}{l}{5}^4=\mathrm{625....}\left(\text{Given}\right)\\ 625=5^4\\ {\log }_5\left(625\right)=\mathrm{4....}\left(\begin{array}{l}\text{Applylogarithmic}\\ \text{form}\end{array}\right)\\ {\log }_{5}625=4\end{array}$

Step 3. Conclusion.

The required logarithmic form is ${\log }_{5}625=4$.