Solve for x e^(x/9)-8=6

$e^{\frac{x}{9}} - 8 = 6$

Step 1

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

Add $8$ to both sides of the equation.

$e^{\frac{x}{9}} = 6 + 8$

Add $6$ and $8$ .

$e^{\frac{x}{9}} = 14$

Step 2

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

$\ln (e^{\frac{x}{9}}) = \ln (14)$

Step 3

Expand the left side.

Expand $\ln (e^{\frac{x}{9}})$ by moving $\frac{x}{9}$ outside the logarithm.

$\frac{x}{9} \ln (e) = \ln (14)$

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

$\frac{x}{9} \cdot 1 = \ln (14)$

Multiply $\frac{x}{9}$ by $1$ .

$\frac{x}{9} = \ln (14)$

Step 4

Multiply both sides of the equation by $9$ .

$9 \frac{x}{9} = 9 \ln (14)$

Step 5

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \frac{x}{9} = 9 \ln (14)$

Rewrite the expression.

$x = 9 \ln (14)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = 9 \ln (14)$

Decimal Form:

$x = 23.75151596 \dots$