Trigonometry Examples

$\frac{1}{27 - 3^{x}}$

Step 1

Set the denominator in $\frac{1}{27 - 3^{x}}$ equal to $0$ to find where the expression is undefined.

$27 - 3^{x} = 0$

Step 2

Solve for $x$ .

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Step 2.1

Subtract $27$ from both sides of the equation.

$- 3^{x} = - 27$

Step 2.2

Divide each term in $- 3^{x} = - 27$ by $- 1$ and simplify.

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Step 2.2.1

Divide each term in $- 3^{x} = - 27$ by $- 1$ .

$\frac{- 3^{x}}{- 1} = \frac{- 27}{- 1}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Dividing two negative values results in a positive value.

$\frac{3^{x}}{1} = \frac{- 27}{- 1}$

Step 2.2.2.2

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{- 27}{- 1}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $- 27$ by $- 1$ .

$3^{x} = 27$

Step 2.3

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

$3^{x} = 3^{3}$

Step 2.4

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

$x = 3$

Step 3