Solve for x 8800=6870(0.995)^x+2500

$8800 = 6870 {(0.995)}^{x} + 2500$

Rewrite the equation as $6870 \cdot {0.995}^{x} + 2500 = 8800$ .

$6870 \cdot {0.995}^{x} + 2500 = 8800$

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

Subtract $2500$ from both sides of the equation.

$6870 \cdot {0.995}^{x} = 8800 - 2500$

Subtract $2500$ from $8800$ .

$6870 \cdot {0.995}^{x} = 6300$

Divide each term in $(6870 \cdot {0.995}^{x}) = 6300$ by $6870$ and simplify.

Divide each term in $(6870 \cdot {0.995}^{x}) = 6300$ by $6870$ .

$\frac{(6870 \cdot {0.995}^{x})}{6870} = \frac{6300}{6870}$

Simplify the left side.

Cancel the common factor of $6870$ .

Cancel the common factor.

$\frac{6870 \cdot {0.995}^{x}}{6870} = \frac{6300}{6870}$

Divide ${0.995}^{x}$ by $1$ .

${0.995}^{x} = \frac{6300}{6870}$

Simplify the right side.

Cancel the common factor of $6300$ and $6870$ .

Factor $30$ out of $6300$ .

${0.995}^{x} = \frac{30 (210)}{6870}$

Cancel the common factors.

Factor $30$ out of $6870$ .

${0.995}^{x} = \frac{30 \cdot 210}{30 \cdot 229}$

Cancel the common factor.

${0.995}^{x} = \frac{30 \cdot 210}{30 \cdot 229}$

Rewrite the expression.

${0.995}^{x} = \frac{210}{229}$

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

$\ln ({0.995}^{x}) = \ln (\frac{210}{229})$

Expand $\ln ({0.995}^{x})$ by moving $x$ outside the logarithm.

$x \ln (0.995) = \ln (\frac{210}{229})$

Divide each term in $x \ln (0.995) = \ln (\frac{210}{229})$ by $\ln (0.995)$ and simplify.

Divide each term in $x \ln (0.995) = \ln (\frac{210}{229})$ by $\ln (0.995)$ .

$\frac{x \ln (0.995)}{\ln (0.995)} = \frac{\ln (\frac{210}{229})}{\ln (0.995)}$

Simplify the left side.

Cancel the common factor of $\ln (0.995)$ .

Cancel the common factor.

$\frac{x \ln (0.995)}{\ln (0.995)} = \frac{\ln (\frac{210}{229})}{\ln (0.995)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{210}{229})}{\ln (0.995)}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{210}{229})}{\ln (0.995)}$

Decimal Form:

$x = 17.27955115 \dots$

Solve for x 8800=6870(0.995)^x+2500

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