Questions: Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log (y) = m

Transcript text: Write the equation in exponential form. Assume that all constants are positive and not equal to 1. \[ \log (y)=m \]

Solution

Solution Steps

To convert a logarithmic equation to its exponential form, we use the definition of logarithms. The equation \(\log(y) = m\) can be rewritten in exponential form as \(y = 10^m\), assuming the base of the logarithm is 10.

Step 1: Given Logarithmic Equation

We start with the given logarithmic equation: \[ \log(y) = m \]

Step 2: Convert to Exponential Form

To convert the logarithmic equation to its exponential form, we use the definition of logarithms. The equation \(\log(y) = m\) can be rewritten as: \[ y = 10^m \]

Step 3: Substitute the Given Value

Given \(m = 2\), we substitute this value into the exponential form: \[ y = 10^2 \]

Step 4: Calculate the Result

Calculate the value of \(y\): \[ y = 100 \]