Topic
Q:
Use properties of logarithms to expand the
logarithmic expression as much as possible.
Where possible, evaluate logarithmic
expressions without using a calculator.
\( \log _{b}\left(y z_{z} 1\right) \)
Q:
Найдите значение выражения:
\( (24 \cdot x-2738: x): x \), при \( x=37 \).
Q:
Expanding Logarithmic Expressions. Write each of the following as the sum or difference of
logarithms. In other words, expand each logarithmic expression.
\( \begin{array}{ll}\text { 1. } \log _{12} \frac{x^{2}(x-7)^{3}}{x+2} & \text { 3. } \ln \frac{x y^{2}}{\sqrt{x-3}} \\ \ln 3 x^{5} y & 4 \cdot \log _{5} \frac{6 x^{2}}{11 y^{3} z}\end{array} \)
Q:
4. Reselve por metodo de igualación
\( \begin{array}{l}x+2 y=2 \\ -x+y=10\end{array} \)
Q:
Write each logarithmic equation in exponential form.
\( \begin{array}{lll}\text { 1. } \log _{7} 49=2 & \text { 3. } \log 100000=5 \\ \text { 2. } \log _{9} 729=3 & \text { 4. } \log x=y+5 & \text { 6. } \ln x^{2}=y \\ \end{array} \)
Q:
A. Write each exponential equation in logarithmic form.
\( \begin{array}{lll}\text { 1. } 2^{6}=64 & 3 \cdot 4^{-2}=\frac{1}{16} & \text { 5. } e^{x+2}=2 \\ \text { 2. } 3^{7}=2187 & \text { 4. }\left(\frac{1}{3}\right)^{3}=\frac{1}{27} & \text { 6. } e^{a}=b-2\end{array} \)
Q:
6. \( 81 r+48 m-6 \)
Q:
Write the system of equations and then use a matrix to solve.
6. Raina, Justin, and Kevin sent a total of 118 text messages during class yesterday. Justin sent 7 fewer
messages than Raina. Kevin sent 3 times as many messages as Raina. How many messages did each
student send?
Q:
Write the system of equations and then use a matrix to solve.
5. The Varsity Bearcat football team scored a total of 50 points in one game. They scored 14 times. The
scoring was made up of touchdowns ( 6 points each), PATs ( 1 point each), and field goals ( 3 points
each). They had 3 more touchdowns than field goals. How many of each type of score did the team
have?
Q:
18 Consider the equation \( x^{2}-2 x+r=0 \), where \( r \) is a real parameter.
\( 1^{\circ} \) Calculate \( r \) so that the roots \( x_{1} \) and \( x_{2} \) exist.
\( 2^{\circ} \) Calculate \( r \) so that :
\( \begin{array}{lll}\text { a) } \frac{1}{x_{1}}+\frac{1}{x_{2}}=-\frac{1}{2} & \text {; b) } x_{1}^{2}+x_{2}^{2}=6 & \text {; ce } \frac{1}{x_{1}^{2}}+\frac{1}{x_{2}^{2}}=1 \\ \text { d) }\left(x_{1}-x_{2}\right)^{2}=4 & \text {; e) } \frac{1}{x_{1}-2}+\frac{1}{x_{2}-2}=3\end{array} \)
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