Algebra Examples

$253428 = e^{x + 3} + 2$

Step 1

Rewrite the equation as $e^{x + 3} + 2 = 253428$ .

$e^{x + 3} + 2 = 253428$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the equation.

$e^{x + 3} = 253428 - 2$

Step 2.2

Subtract $2$ from $253428$ .

$e^{x + 3} = 253426$

Step 3

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

$\ln (e^{x + 3}) = \ln (253426)$

Step 4

Expand the left side.

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Step 4.1

Expand $\ln (e^{x + 3})$ by moving $x + 3$ outside the logarithm.

$(x + 3) \ln (e) = \ln (253426)$

Step 4.2

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

$(x + 3) \cdot 1 = \ln (253426)$

Step 4.3

Multiply $x + 3$ by $1$ .

$x + 3 = \ln (253426)$

Step 5

Subtract $3$ from both sides of the equation.

$x = \ln (253426) - 3$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \ln (253426) - 3$

Decimal Form:

$x = 9.44282714 \dots$