Basic Math Examples

$12 = - \log (b)$

Step 1

Rewrite the equation as $- \log (b) = 12$ .

$- \log (b) = 12$

Step 2

Divide each term in $- \log (b) = 12$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- \log (b) = 12$ by $- 1$ .

$\frac{- \log (b)}{- 1} = \frac{12}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{\log (b)}{1} = \frac{12}{- 1}$

Step 2.2.2

Divide $\log (b)$ by $1$ .

$\log (b) = \frac{12}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $12$ by $- 1$ .

$\log (b) = - 12$

Step 3

Rewrite $\log (b) = - 12$ 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 $b^{y} = x$ .

$10^{- 12} = b$

Step 4

Solve for $b$ .

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Step 4.1

Rewrite the equation as $b = 10^{- 12}$ .

$b = 10^{- 12}$

Step 4.2

Simplify $10^{- 12}$ .

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Step 4.2.1

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

$b = \frac{1}{10^{12}}$

Step 4.2.2

Raise $10$ to the power of $12$ .

$b = \frac{1}{1000000000000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$b = \frac{1}{1000000000000}$

Decimal Form:

$b = 1 \cdot 10^{- 12}$