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Write the log equation as an exponential equation. You do not need to solve for
x.

ln(x^(2)+4x+11)=2
Answer:

Write the log equation as an exponential equation. You do not need to solve for $\mathrm{x}$ . $\newline$ $\ln \left(x^{2}+4 x+11\right)=2$ $\newline$ Answer:

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Convert between exponential and logarithmic form: all bases

Full solution

Q. Write the log equation as an exponential equation. You do not need to solve for

\mathrm{x}

.

\newline

\ln \left(x^{2}+4 x+11\right)=2

\newline

Answer:

Identify Base and Components: Identify the base of the natural logarithm and the components of the equation. $\newline$ The natural logarithm $\ln$ corresponds to the base $e$ , where $e$ is the mathematical constant approximately equal to $2.71828$ . The equation $\ln(x^{2}+4x+11)=2$ can be compared to the general form $\ln(x) = y$ , where $x$ is the argument of the logarithm and $y$ is the result.
Convert to Exponential Form: Convert the logarithmic equation to exponential form. $\newline$ The exponential form of the equation $\ln(x) = y$ is $e^y = x$ . Applying this to our equation $\ln(x^{2}+4x+11)=2$ , we get $e^2 = x^{2}+4x+11$ .
Write Final Exponential Equation: Write the final exponential equation. $\newline$ The final exponential equation is $e^{2} = x^{2}+4x+11$ . This is the equivalent exponential form of the given logarithmic equation.

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