Evaluating Logarithms 1
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Question 1 of 4
1. Question
Solve for `x``x=log_4 64`- `x=` (3)
Hint
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Great Work!
Incorrect
Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$Convert the equation to exponent form by first identifying the components$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` $$x$$ $$\log_{\color{#9a00c7}{4}} \color{#00880a}{64}$$ `=` $$x$$ `N` `=` `64` `a` `=` `4` `x` `=` `x` Substitute the components into the exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{64}$$ `=` $${\color{#9a00c7}{4}}^x$$ Make sure that only `x` is on the left side`64` `=` `4^x` `4^3` `=` `4^x` `64=4^3` `3` `=` `x` Equate the exponents since the bases are equal `x` `=` `3` `x=3` -
Question 2 of 4
2. Question
Solve for `x``x=log_8 1`- `x=` (0)
Hint
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Correct!
Incorrect
Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$Convert the equation to exponent form by first identifying the components$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` $$x$$ $$\log_{\color{#9a00c7}{8}} \color{#00880a}{1}$$ `=` $$x$$ `N` `=` `1` `a` `=` `8` `x` `=` `x` Substitute the components into the exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{1}$$ `=` $${\color{#9a00c7}{8}}^x$$ Make sure that only `x` is on the left side`1` `=` `8^x` To make the equation correct, we need to raise `8` to make its value `1`Any number raised to `0` is equal to `1`. Hence, `x=0``x=0` -
Question 3 of 4
3. Question
Solve for `x``x=log_6 (1/36)`- `x=` (-2)
Hint
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Fantastic!
Incorrect
Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$Convert the equation to exponent form by first identifying the components$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` $$x$$ $$\log_{\color{#9a00c7}{6}} \color{#00880a}{\frac{1}{36}}$$ `=` $$x$$ `N` `=` `1/36` `a` `=` `6` `x` `=` `x` Substitute the components into the exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{\frac{1}{36}}$$ `=` $${\color{#9a00c7}{6}}^x$$ Make sure that only `x` is on the left side`1/36` `=` `6^x` `1/(6^2)` `=` `6^x` `36=6^2` `6^(-2)` `=` `6^x` Reciprocate `1/(6^2)` `-2` `=` `x` Equate the exponents since the bases are equal `x` `=` `-2` `x=-2` -
Question 4 of 4
4. Question
Solve for `x``x=log_2 (1/64)`- `x=` (-6)
Hint
Help VideoCorrect
Nice Job!
Incorrect
Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$Convert the equation to exponent form by first identifying the components$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` $$x$$ $$\log_{\color{#9a00c7}{2}} \color{#00880a}{\frac{1}{64}}$$ `=` $$x$$ `N` `=` `1/64` `a` `=` `2` `x` `=` `x` Substitute the components into the exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{\frac{1}{64}}$$ `=` $${\color{#9a00c7}{2}}^x$$ Make sure that only `x` is on the left side`1/64` `=` `2^x` `1/(2^6)` `=` `2^x` `64=2^6` `2^(-6)` `=` `2^x` Reciprocate `1/(2^6)` `-6` `=` `x` Equate the exponents since the bases are equal `x` `=` `-6` `x=-6`
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