Chapter 11: Conics

Convert to logarithmic form:

$$\begin{gathered} ⓐ4^3=64 \\ ⓑ4^{\frac{1}{3}}=\sqrt[3]{4} \\ ⓒ{\left(\frac{1}{2}\right)}^x=\frac{1}{32} \end{gathered}$$

Find the first term and common difference of the sequence with the given terms. Give the formula for the general term.

The third term is four and the tenth term is −38.

In the following exercises, graph each ellipse.

$\frac{x^2}{25}+\frac{y^2}{9}=1.$

Use the Quotient Property to simplify square roots.

(a)$\sqrt{\frac{72x^5}{y^6}}$

(b)$\sqrt[5]{\frac{96r^{11}}{s^5}}$

(c)$\sqrt[6]{\frac{128u^7}{v^{12}}}$

In the following exercises, graph each ellipse.

$x^2+\frac{y^2}{4}=1$

In the following exercises, graph each ellipse.

$\frac{x^2}{9}+y^2=1$

Use the Power Property of Logarithms to write each logarithm as a product of logarithms. Simplify, if possible.

ⓐ ${\log }_2{3}^7$ⓑ $\log x^{20}$

In the following exercises, graph each ellipse.

$4x^2+25y^2=100$

In the following exercises, graph each ellipse.

$16x^2+9y^2=144$

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{27p^{2}q}{108p^4{q}^3}}$

(b)$\sqrt[3]{\frac{16c^5{d}^7}{250c^2{d}^2}}$

(c)$\sqrt[6]{\frac{2m^9{n}^7}{128m^{3}n}}$