Solve for a -3e^(7a+9)+6=-6

$- 3 e^{7 a + 9} + 6 = - 6$

Step 1

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

Subtract $6$ from both sides of the equation.

$- 3 e^{7 a + 9} = - 6 - 6$

Subtract $6$ from $- 6$ .

$- 3 e^{7 a + 9} = - 12$

Step 2

Divide each term in $- 3 e^{7 a + 9} = - 12$ by $- 3$ and simplify.

Divide each term in $- 3 e^{7 a + 9} = - 12$ by $- 3$ .

$\frac{- 3 e^{7 a + 9}}{- 3} = \frac{- 12}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 e^{7 a + 9}}{- 3} = \frac{- 12}{- 3}$

Divide $e^{7 a + 9}$ by $1$ .

$e^{7 a + 9} = \frac{- 12}{- 3}$

Simplify the right side.

Divide $- 12$ by $- 3$ .

$e^{7 a + 9} = 4$

Step 3

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

$\ln (e^{7 a + 9}) = \ln (4)$

Step 4

Expand the left side.

Expand $\ln (e^{7 a + 9})$ by moving $7 a + 9$ outside the logarithm.

$(7 a + 9) \ln (e) = \ln (4)$

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

$(7 a + 9) \cdot 1 = \ln (4)$

Multiply $7 a + 9$ by $1$ .

$7 a + 9 = \ln (4)$

Step 5

Subtract $9$ from both sides of the equation.

$7 a = \ln (4) - 9$

Step 6

Divide each term in $7 a = \ln (4) - 9$ by $7$ and simplify.

Divide each term in $7 a = \ln (4) - 9$ by $7$ .

$\frac{7 a}{7} = \frac{\ln (4)}{7} + \frac{- 9}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 a}{7} = \frac{\ln (4)}{7} + \frac{- 9}{7}$

Divide $a$ by $1$ .

$a = \frac{\ln (4)}{7} + \frac{- 9}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$a = \frac{\ln (4)}{7} - \frac{9}{7}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$a = \frac{\ln (4)}{7} - \frac{9}{7}$

Decimal Form:

$a = - 1.08767223 \dots$

Solve for a -3e^(7a+9)+6=-6

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