Questions: Write the following equation in logarithmic terms. Do not simplify your answer. 3^x = y

Solution Steps

To express the equation \(3^x = y\) in logarithmic terms, we need to use the definition of a logarithm. The logarithm base 3 of \(y\) is equal to \(x\), which can be written as \(x = \log_3(y)\).

We start with the equation \(3^x = y\). To express this in logarithmic form, we recognize that the logarithm base 3 of \(y\) gives us \(x\).

Using the definition of logarithms, we can rewrite the equation as: \[ x = \log_3(y) \]

Using the change of base formula for logarithms, we can express \(\log_3(y)\) in terms of natural logarithms: \[ \log_3(y) = \frac{\log(y)}{\log(3)} \] Thus, we can rewrite our equation as: \[ x = \frac{\log(y)}{\log(3)} \]

Final Answer