Finite Math Examples

$e^{8 - 5 x} = 1704$

Step 1

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

$\ln (e^{8 - 5 x}) = \ln (1704)$

Step 2

Expand the left side.

Tap for more steps...

Step 2.1

Expand $\ln (e^{8 - 5 x})$ by moving $8 - 5 x$ outside the logarithm.

$(8 - 5 x) \ln (e) = \ln (1704)$

Step 2.2

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

$(8 - 5 x) \cdot 1 = \ln (1704)$

Step 2.3

Multiply $8 - 5 x$ by $1$ .

$8 - 5 x = \ln (1704)$

Step 3

Subtract $8$ from both sides of the equation.

$- 5 x = \ln (1704) - 8$

Step 4

Divide each term in $- 5 x = \ln (1704) - 8$ by $- 5$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 5 x = \ln (1704) - 8$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{\ln (1704)}{- 5} + \frac{- 8}{- 5}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 5$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{\ln (1704)}{- 5} + \frac{- 8}{- 5}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (1704)}{- 5} + \frac{- 8}{- 5}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Simplify each term.

Tap for more steps...

Step 4.3.1.1

Move the negative in front of the fraction.

$x = - \frac{\ln (1704)}{5} + \frac{- 8}{- 5}$

Step 4.3.1.2

Dividing two negative values results in a positive value.

$x = - \frac{\ln (1704)}{5} + \frac{8}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\ln (1704)}{5} + \frac{8}{5}$

Decimal Form:

$x = 0.11185325 \dots$