Algebra Examples

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

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

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

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $- (\log (x) - 2) = 0$ .

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

Step 1.2.2

Solve for $x$ .

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Step 1.2.2.1

Simplify $- (\log (x) - 2)$ .

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Step 1.2.2.1.1

Apply the distributive property.

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

Step 1.2.2.1.2

Multiply $- 1$ by $- 2$ .

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

Step 1.2.2.2

Subtract $2$ from both sides of the equation.

$- \log (x) = - 2$

Step 1.2.2.3

Divide each term in $- \log (x) = - 2$ by $- 1$ and simplify.

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Step 1.2.2.3.1

Divide each term in $- \log (x) = - 2$ by $- 1$ .

$\frac{- \log (x)}{- 1} = \frac{- 2}{- 1}$

Step 1.2.2.3.2

Simplify the left side.

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Step 1.2.2.3.2.1

Dividing two negative values results in a positive value.

$\frac{\log (x)}{1} = \frac{- 2}{- 1}$

Step 1.2.2.3.2.2

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

$\log (x) = \frac{- 2}{- 1}$

Step 1.2.2.3.3

Simplify the right side.

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Step 1.2.2.3.3.1

Divide $- 2$ by $- 1$ .

$\log (x) = 2$

Step 1.2.2.4

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

$10^{2} = x$

Step 1.2.2.5

Solve for $x$ .

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Step 1.2.2.5.1

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

$x = 10^{2}$

Step 1.2.2.5.2

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

$x = 100$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(100, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - (\log (0) - 2)$

Step 2.2

Solve the equation.

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Step 2.2.1

The logarithm of zero is undefined.

$y = Undefined$

Step 2.2.2

Remove parentheses.

$y = - (\log (0) - 2)$

Step 2.2.3

The equation cannot be solved because it is undefined.

$Undefined$

Step 2.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(100, 0)$

y-intercept(s): $None$

Step 4