Converting between natural logarithmic and exponential equations

Rewrite each equation as requested.
(a) Rewrite as an exponential equation.
$\ln x = 6$
(b) Rewrite as a logarithmic equation.
$e^{9} = y$
(a) $◻$
(b)

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Final Answer: \n(a) The exponential form of the equation $\ln x = 6$ is $e^{6} = x$ , which gives $x \approx 403.43$ . \n(b) The logarithmic form of the equation $e^{9} = y$ is $\ln y = 9$ , which gives $y \approx 8103.08$ .

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Step 1 ：Given the equation $\ln x = 6$ , we can rewrite it in exponential form as $e^{6} = x$ .

Step 2 ：Calculating $e^{6}$ , we find that $x \approx 403.43$ .

Step 3 ：Given the equation $e^{9} = y$ , we can rewrite it in logarithmic form as $\ln y = 9$ .

Step 4 ：Calculating $e^{9}$ , we find that $y \approx 8103.08$ .

Step 5 ：Final Answer: \n(a) The exponential form of the equation $\ln x = 6$ is $e^{6} = x$ , which gives $x \approx 403.43$ . \n(b) The logarithmic form of the equation $e^{9} = y$ is $\ln y = 9$ , which gives $y \approx 8103.08$ .

Converting between natural logarithmic and exponential equations Rewrite each equation as requested.(a) Rewrite as an exponential equation.ln⁡x=6(b) Rewrite as a logarithmic equation.e9=y(a) ◻(b)

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Converting between natural logarithmic and exponential equations

Rewrite each equation as requested.
(a) Rewrite as an exponential equation.
$\ln x = 6$
(b) Rewrite as a logarithmic equation.
$e^{9} = y$
(a) $◻$
(b)