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Converting Between Logarithmic and Exponent Form>
Converting Between Logarithmic and Exponent Form 1Converting Between Logarithmic and Exponent Form 1
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Question 1 of 4
1. Question
Convert into logarithmic form`3^4=81`Hint
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Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$First, identify the components of the equation that is given in exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{81}$$ `=` $${\color{#9a00c7}{3}}^4$$ `N` `=` `81` `a` `=` `3` `x` `=` `4` Substitute the components into the logarithmic form$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` `x` $$\log_{\color{#9a00c7}{3}} \color{#00880a}{81}$$ `=` `4` `log_3 81=4` -
Question 2 of 4
2. Question
Convert into logarithmic form`1/2=2^(-1)`Hint
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Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$First, identify the components of the equation that is given in exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{\frac{1}{2}}$$ `=` $${\color{#9a00c7}{2}}^{-1}$$ `N` `=` `1/2` `a` `=` `2` `x` `=` `-1` Substitute the components into the logarithmic form$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` `x` $$\log_{\color{#9a00c7}{2}} \color{#00880a}{\frac{1}{2}}$$ `=` `-1` `log_2 (1/2)=-1` -
Question 3 of 4
3. Question
Convert into logarithmic form`25^(3/2)=125`Hint
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Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$First, identify the components of the equation that is given in exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{125}$$ `=` $${\color{#9a00c7}{25}}^{\frac{3}{2}}$$ `N` `=` `125` `a` `=` `25` `x` `=` `3/2` Substitute the components into the logarithmic form$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` `x` $$\log_{\color{#9a00c7}{25}} \color{#00880a}{125}$$ `=` `3/2` `log_25 125=3/2` -
Question 4 of 4
4. Question
Convert into logarithmic form`16^(3/4)=8`Hint
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Exponent Form
$$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$$Logarithmic Form
$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$$First, identify the components of the equation that is given in exponent form$$\color{#00880a}{N}$$ `=` $${\color{#9a00c7}{a}}^x$$ $$\color{#00880a}{8}$$ `=` $${\color{#9a00c7}{16}}^{\frac{3}{4}}$$ `N` `=` `8` `a` `=` `16` `x` `=` `3/4` Substitute the components into the logarithmic form$$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$$ `=` `x` $$\log_{\color{#9a00c7}{16}} \color{#00880a}{8}$$ `=` `3/4` `log_16 8=3/4`
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