Trigonometry Examples

$- 3^{x} = \frac{1}{8}$

Step 1

Divide each term in $- 3^{x} = \frac{1}{8}$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- 3^{x} = \frac{1}{8}$ by $- 1$ .

$\frac{- 3^{x}}{- 1} = \frac{\frac{1}{8}}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{3^{x}}{1} = \frac{\frac{1}{8}}{- 1}$

Step 1.2.2

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

$3^{x} = \frac{\frac{1}{8}}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative one from the denominator of $\frac{\frac{1}{8}}{- 1}$ .

$3^{x} = - 1 \cdot \frac{1}{8}$

Step 1.3.2

Rewrite $- 1 \cdot \frac{1}{8}$ as $- \frac{1}{8}$ .

$3^{x} = - \frac{1}{8}$

Step 2

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

$\ln (3^{x}) = \ln (- \frac{1}{8})$

Step 3

The equation cannot be solved because $\ln (- \frac{1}{8})$ is undefined.

Undefined

Step 4

There is no solution for $3^{x} = - \frac{1}{8}$

No solution