Finite Math Examples

$\log (1.34 - x) = - 1$

Step 1

Rewrite $\log (1.34 - x) = - 1$ 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 $b^{y} = x$ .

$10^{- 1} = 1.34 - x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $1.34 - x = 10^{- 1}$ .

$1.34 - x = 10^{- 1}$

Step 2.2

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

$1.34 - x = \frac{1}{10}$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

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Step 2.3.1

Subtract $1.34$ from both sides of the equation.

$- x = \frac{1}{10} - 1.34$

Step 2.3.2

To write $- 1.34$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- x = \frac{1}{10} - 1.34 \cdot \frac{10}{10}$

Step 2.3.3

Combine $- 1.34$ and $\frac{10}{10}$ .

$- x = \frac{1}{10} + \frac{- 1.34 \cdot 10}{10}$

Step 2.3.4

Combine the numerators over the common denominator.

$- x = \frac{1 - 1.34 \cdot 10}{10}$

Step 2.3.5

Simplify the numerator.

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Step 2.3.5.1

Multiply $- 1.34$ by $10$ .

$- x = \frac{1 - 13.4}{10}$

Step 2.3.5.2

Subtract $13.4$ from $1$ .

$- x = \frac{- 12.4}{10}$

Step 2.3.6

Divide $- 12.4$ by $10$ .

$- x = - 1.24$

Step 2.4

Divide each term in $- x = - 1.24$ by $- 1$ and simplify.

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Step 2.4.1

Divide each term in $- x = - 1.24$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 1.24}{- 1}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 1.24}{- 1}$

Step 2.4.2.2

Divide $x$ by $1$ .

$x = \frac{- 1.24}{- 1}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 1.24$ by $- 1$ .

$x = 1.24$