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