Trigonometry Examples

$5 {(0.5)}^{x} + 1 = 21$

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.

$5 \cdot {0.5}^{x} = 21 - 1$

Step 1.2

Subtract $1$ from $21$ .

$5 \cdot {0.5}^{x} = 20$

Step 2

Divide each term in $5 \cdot {0.5}^{x} = 20$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 \cdot {0.5}^{x} = 20$ by $5$ .

$\frac{5 \cdot {0.5}^{x}}{5} = \frac{20}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 \cdot {0.5}^{x}}{5} = \frac{20}{5}$

Step 2.2.1.2

Divide ${0.5}^{x}$ by $1$ .

${0.5}^{x} = \frac{20}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $20$ by $5$ .

${0.5}^{x} = 4$

Step 3

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

$\ln ({0.5}^{x}) = \ln (4)$

Step 4

Expand $\ln ({0.5}^{x})$ by moving $x$ outside the logarithm.

$x \ln (0.5) = \ln (4)$

Step 5

Divide each term in $x \ln (0.5) = \ln (4)$ by $\ln (0.5)$ and simplify.

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Step 5.1

Divide each term in $x \ln (0.5) = \ln (4)$ by $\ln (0.5)$ .

$\frac{x \ln (0.5)}{\ln (0.5)} = \frac{\ln (4)}{\ln (0.5)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (0.5)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (0.5)}{\ln (0.5)} = \frac{\ln (4)}{\ln (0.5)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (4)}{\ln (0.5)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (4)}{\ln (0.5)}$

Decimal Form:

$x = - 2$