Questions: Write the equation in its equivalent logarithmic form. 7^2=49 What is the equivalent logarithmic form of the equation?

Transcript text: Write the equation in its equivalent logarithmic form. \[ 7^{2}=49 \] What is the equivalent logarithmic form of the equation? $\square$

Solution

Solution Steps

To convert an exponential equation to its equivalent logarithmic form, we use the relationship between exponents and logarithms. The equation $ a^b = c $ can be rewritten in logarithmic form as $ \log_a(c) = b $. Applying this to the given equation $ 7^2 = 49 $, we can express it as a logarithm.

Step 1: Identify the Exponential Equation

The given exponential equation is $ 7^2 = 49 $.

Step 2: Convert to Logarithmic Form

To convert the exponential equation $ a^b = c $ to its logarithmic form, we use the formula $ \log_a(c) = b $. Applying this to our equation, we have: \[ \log_7(49) = 2 \]

Step 3: Verify the Logarithmic Form

The calculation confirms that the logarithmic form of the equation $ 7^2 = 49 $ is indeed $ \log_7(49) = 2 $.