Finite Math Examples

$e^{6 x - 7} - 5 = 12464$

Step 1

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

Tap for more steps...

Step 1.1

Add $5$ to both sides of the equation.

$e^{6 x - 7} = 12464 + 5$

Step 1.2

Add $12464$ and $5$ .

$e^{6 x - 7} = 12469$

Step 2

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

$\ln (e^{6 x - 7}) = \ln (12469)$

Step 3

Expand the left side.

Tap for more steps...

Step 3.1

Expand $\ln (e^{6 x - 7})$ by moving $6 x - 7$ outside the logarithm.

$(6 x - 7) \ln (e) = \ln (12469)$

Step 3.2

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

$(6 x - 7) \cdot 1 = \ln (12469)$

Step 3.3

Multiply $6 x - 7$ by $1$ .

$6 x - 7 = \ln (12469)$

Step 4

Add $7$ to both sides of the equation.

$6 x = \ln (12469) + 7$

Step 5

Divide each term in $6 x = \ln (12469) + 7$ by $6$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $6 x = \ln (12469) + 7$ by $6$ .

$\frac{6 x}{6} = \frac{\ln (12469)}{6} + \frac{7}{6}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{\ln (12469)}{6} + \frac{7}{6}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (12469)}{6} + \frac{7}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (12469)}{6} + \frac{7}{6}$

Decimal Form:

$x = 2.73850014 \dots$