Precalculus Examples

$350 - {(1.71)}^{x} = 0$

Step 1

Subtract $350$ from both sides of the equation.

$- {1.71}^{x} = - 350$

Step 2

Divide each term in $- {1.71}^{x} = - 350$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- {1.71}^{x} = - 350$ by $- 1$ .

$\frac{- {1.71}^{x}}{- 1} = \frac{- 350}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{{1.71}^{x}}{1} = \frac{- 350}{- 1}$

Step 2.2.2

Divide ${1.71}^{x}$ by $1$ .

${1.71}^{x} = \frac{- 350}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 350$ by $- 1$ .

${1.71}^{x} = 350$

Step 3

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

$\ln ({1.71}^{x}) = \ln (350)$

Step 4

Expand $\ln ({1.71}^{x})$ by moving $x$ outside the logarithm.

$x \ln (1.71) = \ln (350)$

Step 5

Divide each term in $x \ln (1.71) = \ln (350)$ by $\ln (1.71)$ and simplify.

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Step 5.1

Divide each term in $x \ln (1.71) = \ln (350)$ by $\ln (1.71)$ .

$\frac{x \ln (1.71)}{\ln (1.71)} = \frac{\ln (350)}{\ln (1.71)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1.71)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (1.71)}{\ln (1.71)} = \frac{\ln (350)}{\ln (1.71)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (350)}{\ln (1.71)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (350)}{\ln (1.71)}$

Decimal Form:

$x = 10.91892924 \dots$