Trigonometry Examples

$y = \log (x) + 2$

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

Subtract $2$ from both sides of the equation.

$\log (x) = - 2$

Step 1.2.3

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 1.2.4

Solve for $x$ .

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Step 1.2.4.1

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

$x = 10^{- 2}$

Step 1.2.4.2

Simplify $10^{- 2}$ .

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Step 1.2.4.2.1

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

$x = \frac{1}{10^{2}}$

Step 1.2.4.2.2

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

$x = \frac{1}{100}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{100}, 0)$

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): $(\frac{1}{100}, 0)$

y-intercept(s): $None$

Step 4