Finite Math Examples

$\log (\frac{x}{12}) = - 0.875$

Step 1

Rewrite $\log (\frac{x}{12}) = - 0.875$ 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 $b^{y} = x$ .

$10^{- 0.875} = \frac{x}{12}$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $\frac{x}{12} = 10^{- 0.875}$ .

$\frac{x}{12} = 10^{- 0.875}$

Step 2.2

Multiply both sides of the equation by $12$ .

$12 \frac{x}{12} = 12 \cdot 10^{- 0.875}$

Step 2.3

Simplify both sides of the equation.

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Step 2.3.1

Simplify the left side.

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Step 2.3.1.1

Cancel the common factor of $12$ .

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Step 2.3.1.1.1

Cancel the common factor.

$12 \frac{x}{12} = 12 \cdot 10^{- 0.875}$

Step 2.3.1.1.2

Rewrite the expression.

$x = 12 \cdot 10^{- 0.875}$

Step 2.3.2

Simplify the right side.

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Step 2.3.2.1

Simplify $12 \cdot 10^{- 0.875}$ .

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Step 2.3.2.1.1

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

$x = 12 \cdot \frac{1}{10^{0.875}}$

Step 2.3.2.1.2

Raise $10$ to the power of $0.875$ .

$x = 12 \cdot \frac{1}{7.49894209}$

Step 2.3.2.1.3

Divide $1$ by $7.49894209$ .

$x = 12 \cdot 0.13335214$

Step 2.3.2.1.4

Multiply $12$ by $0.13335214$ .

$x = 1.60022571$