Problem 19 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The equivalent logarithmic form of the exponential equation \(7^{y}=200\) is \(\log_{7}(200) = y\).

Step 1: Identify the base of the exponent

The base of the exponent in the given equation is 7. This is represented as \(b\) in the general formula. So, \(b = 7\).

Step 2: Identify the value of the exponent

The value of the exponent is \(y\), which is \(x\) in the general formula. So, \(x = y\).

Step 3: Identify the result of the exponentiation

The result of exponentiation is 200. In the general formula this is represented as \(y\). So, \(y = 200\).

Step 4: Write the logarithmic form

By inserting values into the general formula for converting an exponential form to a logarithmic form \(\log_{b}(y) = x\), the equivalent logarithmic form of the given exponential equation \(7^{y}=200\) is \(\log_{7}(200) = y\)