Precalculus Examples

$4^{x} = 1$

Step 1

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

$\ln (4^{x}) = \ln (1)$

Step 2

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

$x \ln (4) = \ln (1)$

Step 3

Simplify the right side.

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Step 3.1

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

$x \ln (4) = 0$

Step 4

Divide each term in $x \ln (4) = 0$ by $\ln (4)$ and simplify.

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Step 4.1

Divide each term in $x \ln (4) = 0$ by $\ln (4)$ .

$\frac{x \ln (4)}{\ln (4)} = \frac{0}{\ln (4)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $\ln (4)$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{0}{\ln (4)}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{\ln (4)}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Rewrite $\ln (4)$ as $\ln (2^{2})$ .

$x = \frac{0}{\ln (2^{2})}$

Step 4.3.2

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

$x = \frac{0}{2 \ln (2)}$

Step 4.3.3

Cancel the common factor of $0$ and $2$ .

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Step 4.3.3.1

Factor $2$ out of $0$ .

$x = \frac{2 (0)}{2 \ln (2)}$

Step 4.3.3.2

Cancel the common factors.

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Step 4.3.3.2.1

Factor $2$ out of $2 \ln (2)$ .

$x = \frac{2 (0)}{2 (\ln (2))}$

Step 4.3.3.2.2

Cancel the common factor.

$x = \frac{2 \cdot 0}{2 \ln (2)}$

Step 4.3.3.2.3

Rewrite the expression.

$x = \frac{0}{\ln (2)}$

Step 4.3.4

Divide $0$ by $\ln (2)$ .

$x = 0$