Finite Math Examples

$15500 = 4 {(1 + \frac{5.75}{30000})}^{30000 \cdot x}$

Step 1

Rewrite the equation as $4 {(1 + \frac{5.75}{30000})}^{30000 \cdot x} = 15500$ .

$4 {(1 + \frac{5.75}{30000})}^{30000 \cdot x} = 15500$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Divide $5.75$ by $30000$ .

$4 {(1 + 0.000191\overline{6})}^{30000 \cdot x} = 15500$

Step 2.2

Add $1$ and $0.000191\overline{6}$ .

$4 \cdot {1.000191\overline{6}}^{30000 \cdot x} = 15500$

Step 3

Divide each term in $4 \cdot {1.000191\overline{6}}^{30000 \cdot x} = 15500$ by $4$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $4 \cdot {1.000191\overline{6}}^{30000 \cdot x} = 15500$ by $4$ .

$\frac{4 \cdot {1.000191\overline{6}}^{30000 \cdot x}}{4} = \frac{15500}{4}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{4 \cdot {1.000191\overline{6}}^{30000 \cdot x}}{4} = \frac{15500}{4}$

Step 3.2.1.2

Divide ${1.000191\overline{6}}^{30000 \cdot x}$ by $1$ .

${1.000191\overline{6}}^{30000 \cdot x} = \frac{15500}{4}$

${1.000191\overline{6}}^{30000 x} = \frac{15500}{4}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $15500$ by $4$ .

${1.000191\overline{6}}^{30000 x} = 3875$

Step 4

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

$\ln ({1.000191\overline{6}}^{30000 x}) = \ln (3875)$

Step 5

Expand $\ln ({1.000191\overline{6}}^{30000 x})$ by moving $30000 x$ outside the logarithm.

$30000 x \ln (1.000191\overline{6}) = \ln (3875)$

Step 6

Divide each term in $30000 x \ln (1.000191\overline{6}) = \ln (3875)$ by $30000 \ln (1.000191\overline{6})$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $30000 x \ln (1.000191\overline{6}) = \ln (3875)$ by $30000 \ln (1.000191\overline{6})$ .

$\frac{30000 x \ln (1.000191\overline{6})}{30000 \ln (1.000191\overline{6})} = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $30000$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{30000 x \ln (1.000191\overline{6})}{30000 \ln (1.000191\overline{6})} = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Step 6.2.1.2

Rewrite the expression.

$\frac{x \ln (1.000191\overline{6})}{\ln (1.000191\overline{6})} = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Step 6.2.2

Cancel the common factor of $\ln (1.000191\overline{6})$ .

Tap for more steps...

Step 6.2.2.1

Cancel the common factor.

$\frac{x \ln (1.000191\overline{6})}{\ln (1.000191\overline{6})} = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Step 6.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (3875)}{30000 \ln (1.000191\overline{6})}$

Decimal Form:

$x = 1.43705960 \dots$