Trigonometry Examples

$\frac{\log (x) \cdot 1}{6} = - 1$

Step 1

Multiply both sides of the equation by $6$ .

$6 \frac{\log (x) \cdot 1}{6} = 6 \cdot - 1$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $6 \frac{\log (x) \cdot 1}{6}$ .

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Step 2.1.1.1

Cancel the common factor of $6$ .

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Step 2.1.1.1.1

Cancel the common factor.

$6 \frac{\log (x) \cdot 1}{6} = 6 \cdot - 1$

Step 2.1.1.1.2

Rewrite the expression.

$\log (x) \cdot 1 = 6 \cdot - 1$

Step 2.1.1.2

Multiply $\log (x)$ by $1$ .

$\log (x) = 6 \cdot - 1$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $6$ by $- 1$ .

$\log (x) = - 6$

Step 3

Rewrite $\log (x) = - 6$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{- 6} = x$

Step 4

Solve for $x$ .

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Step 4.1

Rewrite the equation as $x = 10^{- 6}$ .

$x = 10^{- 6}$

Step 4.2

Simplify $10^{- 6}$ .

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Step 4.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$x = \frac{1}{10^{6}}$

Step 4.2.2

Raise $10$ to the power of $6$ .

$x = \frac{1}{1000000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{1000000}$

Decimal Form:

$x = 1 \cdot 10^{- 6}$