Finite Math Examples

$f (x) = 5 \log (x - 2)$

Step 1

Set $5 \log (x - 2)$ equal to $0$ .

$5 \log (x - 2) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Divide each term in $5 \log (x - 2) = 0$ by $5$ and simplify.

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Step 2.1.1

Divide each term in $5 \log (x - 2) = 0$ by $5$ .

$\frac{5 \log (x - 2)}{5} = \frac{0}{5}$

Step 2.1.2

Simplify the left side.

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Step 2.1.2.1

Cancel the common factor of $5$ .

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Step 2.1.2.1.1

Cancel the common factor.

$\frac{5 \log (x - 2)}{5} = \frac{0}{5}$

Step 2.1.2.1.2

Divide $\log (x - 2)$ by $1$ .

$\log (x - 2) = \frac{0}{5}$

Step 2.1.3

Simplify the right side.

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Step 2.1.3.1

Divide $0$ by $5$ .

$\log (x - 2) = 0$

Step 2.2

Rewrite $\log (x - 2) = 0$ 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 $b^{y} = x$ .

$10^{0} = x - 2$

Step 2.3

Solve for $x$ .

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Step 2.3.1

Rewrite the equation as $x - 2 = 10^{0}$ .

$x - 2 = 10^{0}$

Step 2.3.2

Anything raised to $0$ is $1$ .

$x - 2 = 1$

Step 2.3.3

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

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Step 2.3.3.1

Add $2$ to both sides of the equation.

$x = 1 + 2$

Step 2.3.3.2

Add $1$ and $2$ .

$x = 3$

Step 3