Finite Math Examples

$9^{x + 2} = 1$

Step 1

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

$\ln (9^{x + 2}) = \ln (1)$

Step 2

Expand $\ln (9^{x + 2})$ by moving $x + 2$ outside the logarithm.

$(x + 2) \ln (9) = \ln (1)$

Step 3

Simplify the left side.

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Step 3.1

Apply the distributive property.

$x \ln (9) + 2 \ln (9) = \ln (1)$

Step 4

Simplify the right side.

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Step 4.1

The natural logarithm of $1$ is $0$ .

$x \ln (9) + 2 \ln (9) = 0$

Step 5

Subtract $2 \ln (9)$ from both sides of the equation.

$x \ln (9) = - 2 \ln (9)$

Step 6

Divide each term in $x \ln (9) = - 2 \ln (9)$ by $\ln (9)$ and simplify.

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Step 6.1

Divide each term in $x \ln (9) = - 2 \ln (9)$ by $\ln (9)$ .

$\frac{x \ln (9)}{\ln (9)} = \frac{- 2 \ln (9)}{\ln (9)}$

Step 6.2

Simplify the left side.

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Step 6.2.1

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

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Step 6.2.1.1

Cancel the common factor.

$\frac{x \ln (9)}{\ln (9)} = \frac{- 2 \ln (9)}{\ln (9)}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2 \ln (9)}{\ln (9)}$

Step 6.3

Simplify the right side.

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Step 6.3.1

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

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Step 6.3.1.1

Cancel the common factor.

$x = \frac{- 2 \ln (9)}{\ln (9)}$

Step 6.3.1.2

Divide $- 2$ by $1$ .

$x = - 2$