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Chapter 10: Q5. (page 535)

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

Short Answer

Expert verified

The required logarithmic form is $\log_{7} \frac{1}{49} = - 2$ .

Step by step solution

01

Step 1. Write down the given equation.

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

02

Step 2. Converting exponential equation to logarithmic form.

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

$\begin{array}{l} 7^{鈭� 2} = \frac{1}{49} .... (Given) \\ \frac{1}{49} = 7^{鈭� 2} \\ \log_{7} (\frac{1}{49}) = 鈭� 2.... (\begin{array}{l} Applylogarithmic \\ form \end{array}) \\ \log_{7} \frac{1}{49} = 鈭� 2 \end{array}$

03

Step 3. Conclusion.

The required logarithmic form is $\log_{7} \frac{1}{49} = - 2$ .

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