Question

Write the equation $7^{-2}=\frac{1}{49}$ in logarithmic form.

Short answer

The required logarithmic form is ${\log }_7\frac{1}{49}=-2$.

Step-by-step solution

Step 1. Write down the given equation.

The given exponential equation is $7^{-2}=\frac{1}{49}$.

Step 2. Converting exponential equation to logarithmic form.

The logarithmic form of $7^{-2}=\frac{1}{49}$is written as:

$\begin{array}{l}{7}^{-2}=\frac{1}{49}\mathrm{....}\left(\text{Given}\right)\\ \frac{1}{49}=7^{-2}\\ {\log }_7\left(\frac{1}{49}\right)=-\mathrm{2....}\left(\begin{array}{l}\text{Applylogarithmic}\\ \text{form}\end{array}\right)\\ {\log }_7\frac{1}{49}=-2\end{array}$

Step 3. Conclusion.

The required logarithmic form is ${\log }_7\frac{1}{49}=-2$.