Topic
Q:
1.2 Given: \( f(x)=k x^{2}-(k+2) x+k+2+\frac{1}{k}=0 \) where \( k \neq 0 \), determine:
1.2.1 the value(s) of \( k \) for which the function has non -Real roots.
1.2.2 for which value(s) of \( k \) will \( g(x)=\frac{1}{k} \) be a tangent to \( f \).
Q:
Let \( m=7 \)
7. \( \left(m^{2}-9\right) \div 2 \)
Q:
Use propenties of logarithms to condense
the logarithmic expression. Write the
expression as a single logarithm whose
coefficient is 1 . Where possible, evaluate
logarithmic expressions. \( \frac{1}{2} \log _{5} x+\log _{5} y \)
Q:
\( 2 ( \log _ { a } c + \log _ { b } c ) = 9 \log _ { a b } c \)
Q:
Condensing Logarithmic Expressions. Rewrite each of the following logarithmic expressions
using a single logarithm.
\( \begin{array}{ll}\text { 1. } \frac{1}{3} \log _{2} 6+\frac{1}{3} \log _{2} x+\frac{2}{3} \log _{2} y & \text { 3.) } 2 \ln (x+3)+\ln x-\ln (2 x-1)\end{array} \)
Q:
\( \left. \begin{array} { l } { \left. \begin{array} { l } { \frac { 2 x } { 2 } \leq - \frac { 8 } { 2 } } \\ { x \leq - 4 } \end{array} \right. \quad ( - \infty , - 4 ] \cup [ 6 , \infty ) } \\ { + 1 / 2 } \end{array} \right. \)
Q:
Simplify the following expressions:
1.2.1 \( \frac{5}{a}-\frac{5}{a^{2}-a} \)
\( 1.2 .2 \frac{x-1}{\sqrt{x}+1} \)
Q:
Use propertius of logarithms to expand the
logarithmic expression as much as possible.
Where possible, evaluate logarithmic
expressions without using a calculator.
\[ \log _{3}\left(\frac{\sqrt{x}}{9}\right) \]
Q:
\( \frac { x } { 1,2 } = \frac { 5 } { 1 } \Rightarrow x = \)
Q:
Use properties of logarithms to expand the
logarithmic expression as much as possible.
Where possible, evaluate logarithmic
expressions without using a calculator.
\[ \log _{b}\left(y z^{4}\right) \]
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