Question

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the set of all points $(e^{t},t)$, where $t$ is a real number, is the graph of $y=$

Explanation:

Step1: Express \(x\) and \(y\)

Let \(x = e^{t}\) and \(y=t\).

Step2: Solve for \(t\) in terms of \(x\)

Take the natural logarithm of both sides of \(x = e^{t}\). Using the property \(\ln(e^{a})=a\), we get \(\ln(x)=\ln(e^{t})\), so \(t=\ln(x)\).

Step3: Substitute \(t\) with \(y\)

Since \(y = t\), substituting \(t=\ln(x)\) gives \(y=\ln(x)\).

Answer:

\(y = \ln(x)\)