Precalculus Examples

\log (x) = - 3

$\log (x) = - 3$

Step 1

Rewrite

\log (x) = - 3

$\log (x) = - 3$ in exponential form using the definition of a logarithm. If

x

$x$ and

b

$b$ are positive real numbers and

b \neq 1

$b \neq 1$ , then

\log_{b} (x) = y

$\log_{b} (x) = y$ is equivalent to

b^{y} = x

$b^{y} = x$ .

10^{- 3} = x

$10^{- 3} = x$

Step 2

Solve for

x

$x$ .

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Step 2.1

Rewrite the equation as

x = 10^{- 3}

$x = 10^{- 3}$ .

x = 10^{- 3}

$x = 10^{- 3}$

Step 2.2

Simplify

10^{- 3}

$10^{- 3}$ .

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Step 2.2.1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

x = \frac{1}{10^{3}}

$x = \frac{1}{10^{3}}$

Step 2.2.2

Raise

10

$10$ to the power of

3

$3$ .

x = \frac{1}{1000}

$x = \frac{1}{1000}$

x = \frac{1}{1000}

$x = \frac{1}{1000}$

x = \frac{1}{1000}

$x = \frac{1}{1000}$

Step 3

The result can be shown in multiple forms.

Exact Form:

x = \frac{1}{1000}

$x = \frac{1}{1000}$

Decimal Form:

x = 0.001

$x = 0.001$

\log (x) = - 3

$\log (x) = - 3$

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