Solve for x 6200=990(1.115)^x+2900

$6200 = 990 {(1.115)}^{x} + 2900$

Step 1

Rewrite the equation as $990 \cdot {1.115}^{x} + 2900 = 6200$ .

$990 \cdot {1.115}^{x} + 2900 = 6200$

Step 2

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

Subtract $2900$ from both sides of the equation.

$990 \cdot {1.115}^{x} = 6200 - 2900$

Subtract $2900$ from $6200$ .

$990 \cdot {1.115}^{x} = 3300$

Step 3

Divide each term in $(990 \cdot {1.115}^{x}) = 3300$ by $990$ and simplify.

Divide each term in $(990 \cdot {1.115}^{x}) = 3300$ by $990$ .

$\frac{(990 \cdot {1.115}^{x})}{990} = \frac{3300}{990}$

Simplify the left side.

Cancel the common factor of $990$ .

Cancel the common factor.

$\frac{990 \cdot {1.115}^{x}}{990} = \frac{3300}{990}$

Divide ${1.115}^{x}$ by $1$ .

${1.115}^{x} = \frac{3300}{990}$

Simplify the right side.

Cancel the common factor of $3300$ and $990$ .

Factor $330$ out of $3300$ .

${1.115}^{x} = \frac{330 (10)}{990}$

Cancel the common factors.

Factor $330$ out of $990$ .

${1.115}^{x} = \frac{330 \cdot 10}{330 \cdot 3}$

Cancel the common factor.

${1.115}^{x} = \frac{330 \cdot 10}{330 \cdot 3}$

Rewrite the expression.

${1.115}^{x} = \frac{10}{3}$

Step 4

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

$\ln ({1.115}^{x}) = \ln (\frac{10}{3})$

Step 5

Expand $\ln ({1.115}^{x})$ by moving $x$ outside the logarithm.

$x \ln (1.115) = \ln (\frac{10}{3})$

Step 6

Divide each term in $x \ln (1.115) = \ln (\frac{10}{3})$ by $\ln (1.115)$ and simplify.

Divide each term in $x \ln (1.115) = \ln (\frac{10}{3})$ by $\ln (1.115)$ .

$\frac{x \ln (1.115)}{\ln (1.115)} = \frac{\ln (\frac{10}{3})}{\ln (1.115)}$

Simplify the left side.

Cancel the common factor of $\ln (1.115)$ .

Cancel the common factor.

$\frac{x \ln (1.115)}{\ln (1.115)} = \frac{\ln (\frac{10}{3})}{\ln (1.115)}$

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{10}{3})}{\ln (1.115)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (\frac{10}{3})}{\ln (1.115)}$

Decimal Form:

$x = 11.06039581 \dots$

Solve for x 6200=990(1.115)^x+2900

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