Solve for x 1700=2600(0.97)^(x+4)

$1700 = 2600 {(0.97)}^{x + 4}$

Rewrite the equation as $2600 \cdot {0.97}^{x + 4} = 1700$ .

$2600 \cdot {0.97}^{x + 4} = 1700$

Divide each term in $(2600 \cdot {0.97}^{x + 4}) = 1700$ by $2600$ and simplify.

Divide each term in $(2600 \cdot {0.97}^{x + 4}) = 1700$ by $2600$ .

$\frac{(2600 \cdot {0.97}^{x + 4})}{2600} = \frac{1700}{2600}$

Simplify the left side.

Cancel the common factor of $2600$ .

Cancel the common factor.

$\frac{2600 \cdot {0.97}^{x + 4}}{2600} = \frac{1700}{2600}$

Divide ${0.97}^{x + 4}$ by $1$ .

${0.97}^{x + 4} = \frac{1700}{2600}$

Simplify the right side.

Cancel the common factor of $1700$ and $2600$ .

Factor $100$ out of $1700$ .

${0.97}^{x + 4} = \frac{100 (17)}{2600}$

Cancel the common factors.

Factor $100$ out of $2600$ .

${0.97}^{x + 4} = \frac{100 \cdot 17}{100 \cdot 26}$

Cancel the common factor.

${0.97}^{x + 4} = \frac{100 \cdot 17}{100 \cdot 26}$

Rewrite the expression.

${0.97}^{x + 4} = \frac{17}{26}$

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

$\ln ({0.97}^{x + 4}) = \ln (\frac{17}{26})$

Expand $\ln ({0.97}^{x + 4})$ by moving $x + 4$ outside the logarithm.

$(x + 4) \ln (0.97) = \ln (\frac{17}{26})$

Simplify the left side.

Apply the distributive property.

$x \ln (0.97) + 4 \ln (0.97) = \ln (\frac{17}{26})$

Move all the terms containing a logarithm to the left side of the equation.

$x \ln (0.97) + 4 \ln (0.97) - \ln (\frac{17}{26}) = 0$

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

Subtract $4 \ln (0.97)$ from both sides of the equation.

$x \ln (0.97) - \ln (\frac{17}{26}) = - 4 \ln (0.97)$

Add $\ln (\frac{17}{26})$ to both sides of the equation.

$x \ln (0.97) = - 4 \ln (0.97) + \ln (\frac{17}{26})$

Divide each term in $x \ln (0.97) = - 4 \ln (0.97) + \ln (\frac{17}{26})$ by $\ln (0.97)$ and simplify.

Divide each term in $x \ln (0.97) = - 4 \ln (0.97) + \ln (\frac{17}{26})$ by $\ln (0.97)$ .

$\frac{x \ln (0.97)}{\ln (0.97)} = \frac{- 4 \ln (0.97)}{\ln (0.97)} + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

Simplify the left side.

Cancel the common factor of $\ln (0.97)$ .

Cancel the common factor.

$\frac{x \ln (0.97)}{\ln (0.97)} = \frac{- 4 \ln (0.97)}{\ln (0.97)} + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

Divide $x$ by $1$ .

$x = \frac{- 4 \ln (0.97)}{\ln (0.97)} + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

Simplify the right side.

Cancel the common factor of $\ln (0.97)$ .

Cancel the common factor.

$x = \frac{- 4 \ln (0.97)}{\ln (0.97)} + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

Divide $- 4$ by $1$ .

$x = - 4 + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

The result can be shown in multiple forms.

Exact Form:

$x = - 4 + \frac{\ln (\frac{17}{26})}{\ln (0.97)}$

Decimal Form:

$x = 9.94925308 \dots$

Solve for x 1700=2600(0.97)^(x+4)

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