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Chapter 3: Problem 7

Find a number \(y\) such that \(\ln y=4\).

Short Answer

Expert verified
The value of \(y\) that satisfies the equation \(\ln y = 4\) is approximately \(y = e^4 \approx 54.598\).

Step by step solution

01

Writing down the given equation

We are given the equation: \(\ln y = 4\)
02

Express the natural logarithm as an exponent

Since the natural logarithm is the logarithm to the base \(e\), we can rewrite the equation using the property of logarithms that says: \(\ln y = 4 \Rightarrow e^4 = y\)
03

Calculate the value of y

We now simply calculate \(e^4\): \(y = e^4 \approx 54.598\) So, the value of \(y\) that satisfies the equation \(\ln y = 4\) is approximately \(54.598\).

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Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=6^{x}+7 $$

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