Problem 19

Question

Write each equation in its equivalent logarithmic form. $$7^{y}=200$$

Step-by-Step Solution

Verified
Answer
The logarithmic form of the equation \(7^{y}=200\) is \(\log_{7}(200) = y\).
1Step 1 Identify the variables
In the given equation \(7^{y}=200\), 7 is the base \(b\), y is the exponent and 200 is the argument \(x\).
2Step 2 Convert to Logarithmic form
Use the conversion rule to write the equation in logarithmic form. The base of the logarithm is the base of the exponential, the argument of the logarithm is the the number on the other side of the equation and the result of the logarithm is the power of the exponential. Therefore, the equivalent logarithmic form of the equation \(7^{y}=200\) is \(\log_{7}(200) = y\).