Topic
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.
\[ \log _{b}\left(y z^{4}\right) \]
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
\( \begin{array}{l}x+2 y=2 \\ -x+y=10\end{array} \)
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