Trigonometry Examples

${(\frac{1}{16})}^{x} < 2$

Step 1

Apply the product rule to $\frac{1}{16}$ .

$\frac{1^{x}}{16^{x}} < 2$

Step 2

One to any power is one.

$\frac{1}{16^{x}} < 2$

Step 3

Move $16^{x}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$16^{- x} < 2$

Step 4

Create equivalent expressions in the equation that all have equal bases.

$2^{4 (- x)} < 2^{1}$

Step 5

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$4 (- x) < 1$

Step 6

Solve for $x$ .

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Step 6.1

Multiply $- 1$ by $4$ .

$- 4 x < 1$

Step 6.2

Divide each term in $- 4 x < 1$ by $- 4$ and simplify.

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Step 6.2.1

Divide each term in $- 4 x < 1$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 x}{- 4} > \frac{1}{- 4}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $- 4$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} > \frac{1}{- 4}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{1}{- 4}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Move the negative in front of the fraction.

$x > - \frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x > - \frac{1}{4}$

Interval Notation:

$(- \frac{1}{4}, \infty)$

Step 8