Trigonometry Examples

$\log_{100} (x) - 2 \log (y) = \frac{\log (10 \sqrt{x})}{y^{2}}$

Step 1

Move all the terms containing a logarithm to the left side of the equation.

$\log_{100} (x) - \log (y^{2}) - \frac{\log (10 \sqrt{x})}{y^{2}} = 0$

Step 2

To find the end points, substitute the bounds of the $y$ values from the domain into $f (y) = 0$ .

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Step 2.1

Replace the variable $y$ with $0$ in the expression.

$f (0) = 0$

Step 2.2

The final answer is $0$ .

$0$

Step 2.3

Replace the variable $y$ with $\infty$ in the expression.

$f (\infty) = 0$

Step 2.4

The final answer is $0$ .

$0$

Step 3

The end points are $(0, 0), (0, \infty)$ .

$(0, 0), (0, \infty)$

Step 4

The square root can be graphed using the points around the vertex $(0, 0), (0, \infty),$

$\begin{array}{c} x & y \\ 0 & 0 \\ 0 & \infty \end{array}$

Step 5