Finite Math Examples

$1 - 9^{x} = 0.25$

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the equation.

$- 9^{x} = 0.25 - 1$

Step 1.2

Subtract $1$ from $0.25$ .

$- 9^{x} = - 0.75$

Step 2

Divide each term in $- 9^{x} = - 0.75$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- 9^{x} = - 0.75$ by $- 1$ .

$\frac{- 9^{x}}{- 1} = \frac{- 0.75}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{9^{x}}{1} = \frac{- 0.75}{- 1}$

Step 2.2.2

Divide $9^{x}$ by $1$ .

$9^{x} = \frac{- 0.75}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 0.75$ by $- 1$ .

$9^{x} = 0.75$

Step 3

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

$\ln (9^{x}) = \ln (0.75)$

Step 4

Expand $\ln (9^{x})$ by moving $x$ outside the logarithm.

$x \ln (9) = \ln (0.75)$

Step 5

Divide each term in $x \ln (9) = \ln (0.75)$ by $\ln (9)$ and simplify.

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Step 5.1

Divide each term in $x \ln (9) = \ln (0.75)$ by $\ln (9)$ .

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (0.75)}{\ln (9)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (9)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (9)}{\ln (9)} = \frac{\ln (0.75)}{\ln (9)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (0.75)}{\ln (9)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (0.75)}{\ln (9)}$

Decimal Form:

$x = - 0.13092975 \dots$