Finite Math Examples

$\log (102 - 2 x) = 2$

Step 1

Rewrite $\log (102 - 2 x) = 2$ 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 $b^{y} = x$ .

$10^{2} = 102 - 2 x$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $102 - 2 x = 10^{2}$ .

$102 - 2 x = 10^{2}$

Step 2.2

Raise $10$ to the power of $2$ .

$102 - 2 x = 100$

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 $102$ from both sides of the equation.

$- 2 x = 100 - 102$

Step 2.3.2

Subtract $102$ from $100$ .

$- 2 x = - 2$

Step 2.4

Divide each term in $- 2 x = - 2$ by $- 2$ and simplify.

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Step 2.4.1

Divide each term in $- 2 x = - 2$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 2}{- 2}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 2$ by $- 2$ .

$x = 1$