Algebra Examples

$y = e^{x} + 1$

Step 1

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

$e^{x} + 1 = y$

Step 2

Subtract $1$ from both sides of the equation.

$e^{x} = y - 1$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

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

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{x})$ by moving $x$ outside the logarithm.

$x \ln (e) = \ln (y - 1)$

Step 4.2

The natural logarithm of $e$ is $1$ .

$x \cdot 1 = \ln (y - 1)$

Step 4.3

Multiply $x$ by $1$ .

$x = \ln (y - 1)$