Questions: Exponential and Logarithmic Functions Converting between natural logarithmic and exponential equations Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. e^y=9 (b) Rewrite as an exponential equation. ln x=4 (a) (b)

Solution Steps

To convert between exponential and logarithmic equations, use the relationships: \( e^y = x \) is equivalent to \( \ln x = y \), and vice versa. For part (a), convert the exponential equation \( e^y = 9 \) to a logarithmic form. For part (b), convert the logarithmic equation \( \ln x = 4 \) to an exponential form.

Given the equation \( e^y = 9 \), we can rewrite it in logarithmic form. The equivalent logarithmic equation is: \[ y = \ln(9) \approx 2.1972 \]

For the equation \( \ln x = 4 \), we convert it to exponential form. The equivalent exponential equation is: \[ x = e^4 \approx 54.5982 \]

Final Answer