Expanding Log Expressions
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 3 questions completed
Questions:
- 1
- 2
- 3
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- Answered
- Review
-
Question 1 of 3
1. Question
Expand$$\log_{a}{\frac{xy}{z}}$$Hint
Help VideoCorrect
Great Work!
Incorrect
Laws of Logarithms
$$\log_{\color{#9a00c7}{b}} {\color{#00880A}{x}\color{#e65021}{y}}=\log_{\color{#9a00c7}{b}} \color{#00880A}{x} + \log_{\color{#9a00c7}{b}} \color{#e65021}{y}$$$$\log_{\color{#9a00c7}{b}} \frac{\color{#00880A}{x}}{\color{#e65021}{y}}=\log_{\color{#9a00c7}{b}} \color{#00880A}{x}-\log_{\color{#9a00c7}{b}} \color{#e65021}{y}$$Expand the fraction by transforming it into a difference$$\log_{\color{#9a00c7}{a}} \frac{\color{#00880A}{xy}}{\color{#e65021}{z}}$$ `=` $$\log_{\color{#9a00c7}{a}} \color{#00880A}{xy}- \log_{\color{#9a00c7}{a}} \color{#e65021}{z}$$ Expand the first term by transforming it into a sum$$\log_{\color{#9a00c7}{a}} \color{#00880A}{x}\color{#e65021}{y}- \log_a z$$ `=` $$\log_{\color{#9a00c7}{a}} \color{#00880A}{x} + \log_{\color{#9a00c7}{a}} \color{#e65021}{y}- \log_a z$$ $$\log_a x + \log_a y- \log_a z$$ -
Question 2 of 3
2. Question
Expand$$\log_a x\sqrt{x+4}$$Hint
Help VideoCorrect
Correct!
Incorrect
Laws of Logarithms
$$\log_{\color{#9a00c7}{b}} {\color{#00880A}{x}\color{#e65021}{y}}=\log_{\color{#9a00c7}{b}} \color{#00880A}{x} + \log_{\color{#9a00c7}{b}} \color{#e65021}{y}$$$$\log_b x^\color{#004ec4}{p}=\color{#004ec4}{p}\log_b x$$Expand the expression by transforming it into a sum$$\log_{\color{#9a00c7}{a}} \color{#00880A}{x}\color{#e65021}{\sqrt{x+4}}$$ `=` $$\log_{\color{#9a00c7}{a}} \color{#00880A}{x} + \log_{\color{#9a00c7}{a}} \color{#e65021}{\sqrt{x+4}}$$ Expand further by using the following laws$$\log_b x^\color{#004ec4}{p}$$ `=` $$\color{#004ec4}{p}\log_b x$$ `log_a x+log_a sqrt(x+4)` `=` $$\log_a x+\log_a (x+4)^\color{#CC0000}{\frac{1}{2}}$$ Change the surd into an exponent `=` `log_a x+` `1/2``log_a (x+4)` `log_b x^p=p log_b x` $$\log_a x + \frac{1}{2}\log_a (x+4)$$ -
Question 3 of 3
3. Question
Expand$$\log_{a}{\frac{x(y+z)}{a^3}}$$Hint
Help VideoCorrect
Keep Going!
Incorrect
Laws of Logarithms
$$\log_{\color{#9a00c7}{b}} {\color{#00880A}{x}\color{#e65021}{y}}=\log_{\color{#9a00c7}{b}} \color{#00880A}{x} + \log_{\color{#9a00c7}{b}} \color{#e65021}{y}$$$$\log_{\color{#9a00c7}{b}} \frac{\color{#00880A}{x}}{\color{#e65021}{y}}=\log_{\color{#9a00c7}{b}} \color{#00880A}{x} – \log_{\color{#9a00c7}{b}} \color{#e65021}{y}$$$$\log_b x^\color{#004ec4}{p}=\color{#004ec4}{p}\log_b x$$$$\log_{\color{#9a00c7}{b}} \color{#9a00c7}{b}=1$$Expand the fraction by transforming it into a difference$$\log_{\color{#9a00c7}{a}} \frac{\color{#00880A}{x(y+z)}}{\color{#e65021}{a^3}}$$ `=` $$\log_{\color{#9a00c7}{a}} \color{#00880A}{x(y+z)}-\log_{\color{#9a00c7}{a}} \color{#e65021}{a^3}$$ Expand the first term by transforming it into a sum$$\log_{\color{#9a00c7}{a}} \color{#00880A}{x}\color{#e65021}{(y+z)}- \log_a a^3$$ `=` $$\log_{\color{#9a00c7}{a}} \color{#00880A}{x} + \log_{\color{#9a00c7}{a}} \color{#e65021}{(y+z)}- \log_a a^3$$ Expand further by using the following laws$$\log_b x^\color{#004ec4}{p}$$ `=` $$\color{#004ec4}{p}\log_b x$$ $$\log_{\color{#9a00c7}{b}} \color{#9a00c7}{b}$$ `=` $$1$$ `log_a x+log_a (y+z)-log_a a^3` `=` `log_a x+log_a (y+z)-` `3``log_a a` `log_b x^p=p log_b x` `=` `log_a x+log_a (y+z)-3(``1``)` `log_b b=1` `=` `log_a x+log_a (y+z)-3` `log_a x+log_a (y+z)-3`
Quizzes
- Converting Between Logarithmic and Exponent Form 1
- Converting Between Logarithmic and Exponent Form 2
- Evaluating Logarithms 1
- Evaluating Logarithms 2
- Evaluating Logarithms 3
- Expanding Log Expressions
- Simplifying Log Expressions 1
- Simplifying Log Expressions 2
- Simplifying Log Expressions 3
- Change Of Base Formula
- Logarithmic Equations 1
- Logarithmic Equations 2
- Logarithmic Equations 3
- Solving Exponential Equations