Calculus Examples

$\ln (e + x) = 1$

Step 1

To solve for $x$ , rewrite the equation using properties of logarithms.

$e^{\ln (e + x)} = e^{1}$

Step 2

Rewrite $\ln (e + x) = 1$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$e^{1} = e + x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $e + x = e^{1}$ .

$e + x = e$

Step 3.2

Move all terms not containing $x$ to the right side of the equation.

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Step 3.2.1

Subtract $e$ from both sides of the equation.

$x = e - e$

Step 3.2.2

Subtract $e$ from $e$ .

$x = 0$