Finite Math Examples

$6 e^{x} + 5 = 23$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$6 e^{x} = 23 - 5$

Step 1.2

Subtract $5$ from $23$ .

$6 e^{x} = 18$

Step 2

Divide each term in $6 e^{x} = 18$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 e^{x} = 18$ by $6$ .

$\frac{6 e^{x}}{6} = \frac{18}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 e^{x}}{6} = \frac{18}{6}$

Step 2.2.1.2

Divide $e^{x}$ by $1$ .

$e^{x} = \frac{18}{6}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $18$ by $6$ .

$e^{x} = 3$

Step 3

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

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

Step 4

Expand the left side.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Multiply $x$ by $1$ .

$x = \ln (3)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \ln (3)$

Decimal Form:

$x = 1.09861228 \dots$